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Doctoral Thesis in Physics

Semiconductor Quantum Optics at Telecom WavelengthsKATHARINA D. ZEUNER

Stockholm, Sweden 2020www.kth.se

ISBN 978-91-7873-689-8TRITA-SCI-FOU 2020:35

kth royal institute of technology

Katharina D. Zeuner Sem

iconductor Quantum

Optics at Telecom

Wavelengths

KTH

2020

Semiconductor Quantum Optics at Telecom Wavelengths

KATHARINA D. ZEUNER

Doctoral Thesis in Physics

KTH Royal Institute of Technology

Stockholm, Sweden 2020

Academic Dissertation which, with due permission of the KTH Royal Institute of Technology, is submitted for public defence for the Degree of Doctor of Philosophy on Friday the 4th of December 2020, at 9:00 a.m. in Kollegiesalen, Brinellvägen 8, Stockholm.

© Katharina D. Zeuner

Cover page photo: Modified photography of laser beams passing through an optical setup.

ISBN 978-91-7873-689-8

TRITA-SCI-FOU 2020:35

Printed by: Universitetsservice US-AB, Sweden 2020

“Nobody said it was easy.”

Coldplay, The Scientist

Semiconductor Quantum Optics at Telecom Wavelengths

Katharina D. ZeunerAlbanova University Center, Department of Applied Physics, KTH Royal Insti-tute of Technology, SE-106 91 Stockholm, Sweden

AbstractQuantum technologies are an expanding field in physics and engineering con-cerning the development of protocols and devices that enable augmented ornovel applications based on quantum mechanics. This includes amongst othersquantum computation and quantum communication. Quantum computerspromise a computational speed–up based on superposition relevant for opti-mization and simulation problems, as well as for factorizing of large numbers,which poses a threat to our classical encryption schemes. Quantum commu-nication offers a solution to this issue by providing an unconditionally securecommunication channel based on the laws of quantum mechanics. Moreover,quantum communication would allow the exchange of quantum informationbetween remote quantum computers, enabling distributed quantum computing.An infrastructure that links quantum computers or processors is referred toas a quantum network. Stationary quantum bits at the network nodes areused for performing information processing or storing operations, while flyingquantum bits connect the nodes and enable the transfer of quantum informa-tion. Photons are excellent flying quantum bits, as they travel at the speedof light and have a small interaction cross–section. Consequently, quantumnetworks require sources of quantum states of light to provide flying quantumbits. These quantum states of light need to be entangled, indistinguishable andwavelength–matched such that they either experience low transmission losses innetworks or can be interfaced with other quantum technologies like atom–basedquantum memories.In this thesis the emission of single, indistinguishable or entangled photonsfrom single self–assembled optically active semiconductor quantum dots, ourquantum emitter of choice, has been studied. The investigated quantum dotsemit either in the telecom range or close to the D1–transition in Rubidium.The main aspects of the experiments performed in this thesis were to researchthe integrability of the emitters into future quantum networks by making themwavelength–tunable, integrating them into photonic structures and employingresonant excitation schemes in order to generate photons with unprecedentedpurity, indistinguishability or entanglement concurrence.In the telecom range, we study InAsP nanowire quantum dots whose emissionis shifted from the near–infrared range up to the telecom O–band and C–band.Single photon emission is demonstrated with decay times of the quantum dotssimilar to their near–infrared counterparts. Furthermore, InAs/GaAs quantumdots emitting in the telecom C–band are integrated onto piezo–electric sub-strates, and their emission is modulated into sidebands by using commercial

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telecommunication equipment. We generate on–demand single photons using atwo–photon resonant excitation scheme and on–demand entangled photons viaa phonon–assisted resonant scheme.Droplet–etched GaAs quantum dots with emission in the vicinity of the D1–Rubidium transition have been excited via two–photon resonant excitation togenerate single photons with unparalleled purity and highly entangled pho-ton pairs to perform entanglement swapping. Under resonance fluorescence,single and highly indistinguishable photons are extracted. Both resonant exci-tation schemes are theoretically compared to reveal the limitations of the twotechniques. Moreover, these quantum dots are integrated into piezo–tunablebroad–band micro parabolic cavities for an enhanced extraction efficiency.

Key words: quantum dots, single–photons, indistinguishability, entanglement

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Halvledar kvantoptik vid telekom vaglangd

Katharina D. ZeunerAlbanova University Center, Institutionen for tillampad fysik, Kungliga TekniskaHogskolan, SE-106 91 Stockholm, Sverige

SammanfattningKvantteknologi ar ett vaxande falt inom bade teoretisk och tillampad fysik somfokuserar pa att utveckla protokoll och applikationer som utnyttjar kvantmeka-niska fenomen. Exempel pa detta inkluderar kvantdatorer och kvantkommunika-tion. Kvantdatorer utlovar en okad berakningshastighet grundad i superposition,vilket ar relevant for optimerimg och simulering samt faktorisering av storatal vilket utgor ett hot for klassisk kryptering. Kvantkommunikation utgoren losning till detta problem och erbjuder kommunikation vars sakerhet argaranterad av kvantmekanikens lagar. Utover detta mojliggor kvantkommuni-kation utbyte av kvantinformation mellan avlagsna kvantdatorer vilket tillaterutspridning av kvantberakningar. En infrastruktur som mojliggor sammankopp-lingen av kvantdatorer eller kvantprocessorer kallas aven for ett kvantnatverk.Stationara kvantbitar vid noderna av natverket anvands for att forvara ochbehandla kvantinformation medan flygande kvantbitar kopplar samman nodernaoch anvands for utbyte av kvantinformation. Fotoner ar exemplariska flygandekvantbitar da de fardas med ljusets hastighet och har ett lagt interaktions-tvarsnitt . En konsekvens av detta ar att kvantnatverk kraver kvanttillstandav ljus att agera som flygande kvantbitar. Dessa kvantiserade ljustillstand harstranga krav att vara intrasslade, oskiljbara och matcha i vaglangd sa attt deantingen upplever sma forluster vid transport i optiska fiber eller att de matchartill andra kvantteknologier som atom baserade kvantminnen.I denna avhandling har utstralningen av enstaka, oskiljbara eller intrassla-de fotoner studerats fran enstaka sjalvmonterade optiskt aktiva halvledarekvantprickar, var foredragna kvanttillstands genererare. Dessa kvantprickarproducerar fotoner i telekomfrekvens eller nara D1–overgangen i Rubidium.Huvudaspekten av denna avhandling har varit att experimentellt undersokamojligheten att integrera dessa foton kallor i kvantnatverk genom att mojliggoravaglangds–justering, integrera dem i optiska strukturer samt anvanda resonantexcitation for att generera fotoner med ej tidigare skadad renhet, oskiljbarheteller intrassling samstammighet.For frekvenser nara telekomfrekvens undersoks InAsP kvantprickar i nanorormed utstralning skiftad fran nara infrarott till telekom O–band och C–band.Utstralning av enstaka fotoner demonstreras med livsstid for kvantprickar-na jamforbara med deras nara infrarod motsvarigheter. Utover detta har harkvantprickar av InAs/GaAs som utstralar i telekom C–bandet integrerats papiezo–elektriska substrat, dess utstralning modulerats till sidoband med hjalpav komersiell telekommunikationsutrustning och vi generear enstaka fotonerpa begaran genom att anvanda tva foton–resonant excitation och pa begaran

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intrasslade fotoner via en fonon assisterad resonans.Dropetsade GaAs kvantprickar med utstralning nara D1 Rubidium overgangenhar exciterats med hjalp av tva foton–resonans for att generera enstaka fotonermed oovertraffad renhet och intrasslade fotoner som anvandes for att utforaintrasslings overforing. Vid resonant fluorescens kunde enstaka och oskiljbarafotoner utvinnas. Bade resonanta excitations teknikerna jamfors teoretiskt foratt undersoka deras begransningar. Utover detta integreras kvantprickarna papiezo–kontrollerad bredband microparabolisk kavitet for forhojd utkopplingseffektivitet.

Nyckelord: kvantprickar, singelfotoner, oskiljbarhet, intrassling

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Preface

This thesis deals with quantum states of light emitted by epitaxially–grownoptically active semiconductor quantum dots with regard of their integrationinto future quantum networks. Resonant excitation techniques to generatesingle, indistinguishable or entangled photons of highest optical quality havebeen investigated and integration of quantum dot into tunable devices anddevices with enhanced extraction efficiency has been demonstrated. The focusof the thesis was on generating quantum states of light at telecom wavelengthsto ultimately transmit single and entangled photons over long distances inoptical fibers with either InAsP nanowires or InAs/GaAs quantum dots. Besides,experimental work has also been performed on GaAs quantum dots with emissionclose to an atomic transition in Rubidium.

Paper 1. L. Schweickert, K. D. Jons, K. D. Zeuner, S. F. C. da Silva,H. Huang, T. Lettner, M. Reindl, J. Zichi, R. Trotta, A. Rastelliand V. Zwiller, 2018. On-demand generation of background-free singlephotons from a solid-state source. Appl. Phys. Lett. 112 (093106), 1–4.

Paper 2. S. Haffouz, K D. Zeuner, D. Dalacu, P. J. Poole, J. La-pointe, D. Poitras, K. Mnaymneh, X. Wu, M. Couillard, M. Ko-rkusinski, E. Scholl, K. D. Jons, V. Zwiller, and R. L. Williams,2018. Bright Single InAsP Quantum Dots at Telecom Wavelengths in Position-Controlled InP Nanowires: The Role of the Photonic Waveguide. Nano Lett.18, 3047–3052.

Paper 3. K. D. Zeuner, M. Paul, T. Lettner , C. Reuterskiold Hed-lund, L. Schweickert, S. Steinhauer, L. Yang, J. Zichi, M. Hammar,K. D. Jons, and V. Zwiller, 2018. A stable wavelength-tunable triggeredsource of single photons and cascaded photon pairs at the telecom C-band. Appl.Phys. Lett. 112 (173102), 1–5.

Paper 4. E. Scholl,† L. Hanschke,† L. Schweickert,† K. D. Zeuner,M. Reindl, S. F. C. da Silva, T. Lettner, R. Trotta, J. J. Finley,K. Muller, A. Rastelli, V. Zwiller, and K. D. Jons, 2019. ResonanceFluorescence of GaAs Quantum Dots with Near-Unity Photon Indistinguishabil-ity. Nano Lett. 19, 2404–2410.

Paper 5. S. Gyger,† K. D. Zeuner,† K. D. Jons, A. W. Elshaari,M. Paul, S. Popov, C. Reuterskiold Hedlund, M. Hammar, O. Os-zolins, and V. Zwiller, 2019. Reconfigurable frequency coding of triggeredsingle photons in the telecom C-band. Optics Express 27, 14400–14406.

Paper 6. F. Basso Basset,† M. B. Rota,† C. Schimpf,† D. Tedeschi,†K. D. Zeuner, S. F. Covre da Silva, M. Reindl, V. Zwiller, K. D. Jons,A. Rastelli, and R. Trotta, 2019. Entanglement Swapping with Photons

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Generated on Demand by a Quantum Dot. Phys. Rev. Lett. 123 (160501), 1–6.

Paper 7. T. Lettner, K .D. Zeuner, E. Scholl, H. Huang, S. Scharmer,S. F. Covre da Silva, S. Gyger, L. Schweickert, A. Rastelli,K. D. Jons, and V. Zwiller, 2019. GaAs Quantum Dot in a ParabolicMicrocavity Tuned to 87Rb D1. ACS Photonics 7, 29–35.

Paper 8. K. D. Zeuner, K. D. Jons, L. Schweickert, C. Reuter-skiold Hedlund, C. Nunez Lobato, T. Lettner, K. Wang, S. Gyger,E. Scholl, S. Steinhauer, M. Hammar, and V. Zwiller. On—demandgeneration of entangled photon pairs in the telecom C—band for fiber—basedquantum networks. Submitted, tbd.

Paper 9. E. Scholl,† L. Schweickert,† L. Hanschke, K. D. Zeuner, F.Sbresny, T. Lettner, R. Trivedi, M. Reindl, S. F. Covre da Silva,R. Trotta, J. J. Finley, J. Vuckovic, K. Muller, A. Rastelli, V.Zwiller, and K. D. Jons, 2020. The crux of using the cascaded emission ofa 3—level quantum ladder system to generate indistinguishable photons. Phys.Rev. Lett., Accepted, tbd.

December 2020, StockholmKatharina D. Zeuner

†: Authors contributed equally.

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Author contributionsThe main advisor for the project is Prof. Dr. Val Zwiller (VZ). Dr. Klaus Jons(KDJ) acts as co-advisor.

Paper 1. Building of the setup and performing the experiment with KDJ andLucas Schweickert (LS). Input to the manuscript.

Paper 2. Building of the setup with help from KDJ and LS. Participation insample characterization with Sofianne Haffouz (SH), Dan Dalacu (DD) withhelp from Eva Scholl (ES). Analysis of correlation measurements. Input tomanuscript preparation.

Paper 3. Building of the setup with help from KDJ and LS. Sample character-ization with Matthias Paul (MP) and participation in the device fabricationwith KDJ and Thomas Lettner (TL). Performance of the experiments and dataanalysis with KDJ and LS. Preparation of the manuscript with KDJ.

Paper 4. Participation in building the setup with KDJ, ES, and LS. Perfor-mance of the experiments and data analysis with ES, Lukas Hanschke (LH),LS and KDJ. Input to the manuscript.

Paper 5. Building the setup with KDJ and LS. Performance of the experiment,data analysis and writing the manuscript with Samuel Gyger (SG) and inputfrom KDJ.

Paper 6. Building the setup with Francesco Basso Basset (FBB), Michele Rota(MR), Christian Schimpf (CS), Davide Tedeschi (DT), KDJ and Rinaldo Trotta(RT). Performing preliminary measurements with FFB, MR, CS, DT, KDJ andRT. Input to the manuscript.

Paper 7. Performing simulations for the device design with input from TL.Participation in building the setup with KDJ, ES and LS. Data analysis withTL. Input to the manuscript.

Paper 8. Building of the setup with LS and KDJ. Performance of the experimentwith LS and KDJ. Data analysis with help of LS and TL. Preparation of themanuscript with KDJ.

Paper 9. Participation in building the setup with KDJ, ES, and LS and inperforming measurements with ES, LS, LS and KDJ. Input to the manuscript.

Other publicationsThe following papers, although related, are not included in this thesis.

J. Kettler, M. Paul, F. Olbrich, K. D. Zeuner, M. Jetter, P.Michler, 2016. Single-photon and photon pair emission from MOVPE-grownIn(Ga)As quantum dots: shifting the emission wavelength from 1.0 to 1.3 μm.Appl. Phys. B (3) (48),

.

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J. Kettler, M. Paul, F. Olbrich, K. D. Zeuner, M. Jetter, P. Mich-ler, M. Florian, C. Carmesin, F. Jahnke, 2016. Neutral and chargedbiexciton-exciton cascade in near-telecom-wavelength quantum dots. Phys. Rev.B (4) (94),

.

L. Hanschke, L. Schweickert, J. C. Lopez Carreno, E. Scholl, K. D.Zeuner, T. Lettner, E. Zubizarreta Casalengua, M. Reindl, S. F.Covre da Silva, R. Trotta, J. J. Finley, A. Rastelli, E. del Valle,F. P. Laussy, V. Zwiller, K. Muller, and K. D. Jons, 2020. The Originof Antibunching in Resonance Fluorescence. Submitted tbd,

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ConferencesPart of the work in this thesis has been presented at the following internationalconferences and workshops. The presenting author is underlined.

Poster Presentations:

K. D. Zeuner, T. Lettner, A. Elshaari, K. D. Jons, and V. Zwiller.Design of a quantum dot based light source for quantum optics at telecomwavelengths. Okinawa School in Physics 2016: Coherent Quantum Dynamics.Okinawa, 2016.

K. D. Zeuner, M. Paul, T. Lettner , C. Reuterskiold Hedlund,L. Schweickert, S. Steinhauer, L. Yang, J. Zichi, M. Hammar,K. D. Jons, and V. Zwiller. Wavelength-tunable emission of triggered singlephotons at the telecom C-band. Quantum Networks – from building blocks toapplications. Bad Honnef, 2018.

K. D. Zeuner, M. Paul, T. Lettner , C. Reuterskiold Hedlund,L. Schweickert, S. Steinhauer, L. Yang, J. Zichi, M. Hammar,K. D. Jons, and V. Zwiller. Wavelength-tunable emission of triggeredsingle photons at the telecom C-band. 20th International Winterschool on NewDevelopments in Solid State Physics. Mauterndorf, 2018.

K. D. Zeuner, M. Paul, T. Lettner , C. Reuterskiold Hedlund,L. Schweickert, S. Steinhauer, L. Yang, J. Zichi, M. Hammar,K. D. Jons, and V. Zwiller. A stable wavelength–tunable source of triggeredsingle photons at the telecom C-band. 34th international conference on thephysics of semiconductors. Montpellier, 2018.

S. Gyger, K. D. Zeuner, K. D. Jons, A. W. Elshaari , M. Paul,C. Reuterskiold Hedlund, M. Hammar, O. Ozolins, V. Zwiller.Reconfigurable Modulation of of a Quantum Light Source in the telecom C–Band.6th international workshop on “Engineering of Quantum Emitter Properties.Rome, 2018.

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K. D. Zeuner, K. D. Jons, L. Schweickert, C. Reuterskiold Hedlund,C. Nunez Lobato, T. Lettner, K. Wang, S. Gyger, E. Scholl, G.Vall-Llosera, S. Steinhauer, M. Hammar, and V. Zwiller. PhotonicQubits emitted by semiconductor quantum dots for quantum network applica-tions. 7th international workshop on engineering of quantum emitter properties.Berlin, 2019.

Oral presentations:K. D. Zeuner, S. Gyger, K. D. Jons, C. Nunez Lobato, C. Reuter-skiold Hedlund, S. Steinhauer, G. Vall Llosera, K. Wang, M. Ham-mar and V. Zwiller. Photonic qubits emitted by semiconductor quantumdots for quantum network applications . 14th IEEE Nanotechnology materialsand devices conference. Stockholm, 2019.V. Zwiller, K. D. Zeuner, L. Schweickert, T. Lettner, E. Scholl,S. Gyger, J. Zichi, A. Elshaari, S. Steinhauer, M. Hammar, K. D.Jons. Integration of quantum emitters and detectors. SPIE Photonics West.San Francisco, 2020.

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Contents

Abstract v

Sammanfattning vii

Preface ix

List of Abbreviations xviii

Part I - Overview and summary

Chapter 1. Introduction 1

Chapter 2. Photon statistics 52.1. Types of light 52.2. Second–order coherence 72.3. Two–photon interference 82.4. Entanglement 9

Chapter 3. Sources of single and entangled photons at telecomwavelengths 12

3.1. Spontaneous conversion and mixing processes 123.2. Other sources 143.3. Optically active epitaxial semiconductor quantum dots 15

Chapter 4. Photonic structures for quantum dots 264.1. Microcavities 274.2. Waveguiding structures 294.3. Extraction efficiency enhancement at telecom wavelengths 31

Chapter 5. Quantum dot tuning techniques 335.1. Overview of tuning techniques 335.2. Strain tuning 35

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Chapter 6. Devices studied in this thesis 376.1. InAs quantum dots at telecom wavelengths 376.2. InP dots in nanowires emitting at telecom wavelengths 406.3. GaAs quantum dots at Rb wavelength 42

Chapter 7. Cryogenic micro–photoluminescence 457.1. Setup 457.2. Characterization measurements 487.3. Excitation techniques 51

Chapter 8. Correlation spectroscopy measurements 578.1. Auto–correlation measurements 578.2. Hong–Ou–Mandel experiments 598.3. Entanglement measurements 60

Chapter 9. Conclusions and outlook 66

Appendix A. Transmission spectrometers for highly efficientspectral filtering 70

Appendix B. Finestructure optimization of InAs/GaAs quantumdots 74

Appendix C. The Stockholm quantum link 76C.1. Link properties 76

Acknowledgements 80

Bibliography 83

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Part II - Papers

Summary of the papers 115

Paper 1. On-demand generation of background-free singlephotons from a solid-state source 119

Paper 2. Bright Single InAsP Quantum Dots at TelecomWavelengths in Position-Controlled InP Nanowires:The Role of the Photonic Waveguide 125

Paper 3. A stable wavelength-tunable triggered source ofsingle photons and cascaded photon pairs at thetelecom C-band 133

Paper 4. Resonance Fluorescence of GaAs Quantum Dotswith Near-Unity Photon Indistinguishability 141

Paper 5. Reconfigurable frequency coding of triggered singlephotons in the telecom C-band 151

Paper 6. Entanglement Swapping with Photons Generatedon Demand by a Quantum Dot 161

Paper 7. GaAs Quantum Dot in a Parabolic MicrocavityTuned to 87Rb D1 169

Paper 8. On—demand generation of entangled photon pairsin the telecom C—band for fiber—based quantumnetworks 179

Paper 9. The crux of using the cascaded emission of a 3–levelquantum ladder system to generate indistinguishablephotons 191

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List of Abbreviations

AlGaAs Aluminum gallium arsenideBS Non–polarizing beam splitter (50:50, usually)CCD Charge–coupled deviceCW Continuous waveDBR Distributed Bragg reflectorFDTD Finite–difference time domainFSS Finestructure splittingFWM Four–wave mixingGaAs Gallium arsenideHOM Hong–Ou–MandelHeNe Helium–neon laserInAs Indium arsenideInAsP Indium arsenide phosphideInGaAs Indium gallium arsenideInP Indium phosphideMBE molecular beam epitaxyMOVPE metal–organic vapor–phase epitaxyPBS Polarizing beam splitterPL-map Photoluminescence mapPMN–PT Pb

(Mg1/3Nb2/3

)O3–PbTiO3

PZT PbZrO3–PbTiO3

QD Quantum dotRF Resonance fluorescenceSEM Scanning electron microscopeSPDC Spontaneous parametric down conversionSSPD Superconducting single–/strip–photon detectorTMM Transfer matrix methodTPE Two–photon excitationTS Transmission spectrometerX ExcitonXX Biexciton

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Part I

Overview and summary

Chapter 1

Introduction

The first quantum revolution was initiated by scientific discoveries of the wave–particle dualism in the early 20th century [1]. This prompted inventions likethe laser and the transistor, technologies that have significantly contributedto the information age. While the first quantum revolution has allowed us tounderstand quantum physics and, thus, develop novel technologies, the secondquantum revolution is all about applying quantum mechanical rules to controlquantum systems. For example, the first quantum revolution has allowed us tounderstand the wavefunction of electrons in natural atoms, whereas the secondquantum revolution has enabled us to design artificial atoms and manipulatethem at our will. Ultimately, this will lead to the development of technologiesthat are outside of the classical realm.Quantum technologies currently going through research and development areamongst others

1. quantum sensing and metrology [2]–[6] which are expected to result inmore precise measurements,

2. quantum computing [7]–[9] leading to a speed–up for simulation [10] andoptimization problems [11], [12] and

3. quantum communication enabling secure communication [13]–[15] andthe exchange of quantum states.

Based on their computational speed–up due to the quantum principle of super-position, quantum algorithms pose a threat to classical encryption schemes [16],[17]. Here, quantum communication offers a solution by providing a securecommunication channel that is fundamentally protected by quantum physics [18].Quantum key distribution protocols with single [13] or entangled photons [14],[19] are already seeing first demonstrations outside of laboratories [20]–[27]. De-veloping a global quantum network would not only allow secure communicationof sensitive data, but enable the connection of remote quantum computers fordistributed quantum computing and the formation of a quantum internet [28].Photons are the information carriers of choice when considering creating largescale networks, as they provide information transfer at the speed of light, whileexperiencing low losses in optical fibers and exhibiting a small interaction crosssection. Just like classical bits, quantum bits exhibit absorption in the fiberglass material used in the global fiber network for information distribution.

1

2 1. Introduction

Unlike their classical counterparts, quantum bits cannot be amplified, creatingan imperative for quantum repeaters as parts of quantum networks [29], [30].Therefore the flying qubits should on the one hand be wavelength–matchedto the fiber–based infrastructure (wavelengths around 1.31μm or 1.55μm forlowest absorption loss) and on the other hand be able to be interfaced withquantum repeaters. The photons should exhibit high single photon purity andentanglement fidelity to be suitable for quantum key distribution protocols andmoreover a near unity indistinguishability of the photons is required to success-fully perform entanglement swapping operations. Furthermore, high generationrates of on–demand flying qubits are universally beneficial for applications inquantum communication.A variety of processes and material systems to generate quantum states of lightsuitable for quantum communications are under development, amongst othersspontaneous generation processes in non–linear crystals such as spontaneousparametric down conversion, which has historically been the work horse ofentanglement distribution in optical fibers [24], [31]–[34]. The spontaneity ofthe process however, comes with an intrinsic efficiency–versus–purity issue.Typically, the generation rates in these sources have to be kept low in orderto keep the multi–photon pair generation rate to a minimum [35]. Quantumemitters such as atoms and ions [36]–[38], molecules [39]–[41], defects in thesolid state [42] and optically active quantum dots [43], [44] are able to produceonly a single photon or an entangled photon pair. As the transitions used forthe photon generation are discrete and a characteristic recombination time hasto pass before the next emission is possible. The steady advances in quantumdot quality and control have enabled first proof of principle experiments inquantum key distribution in recent years [26], [27], [45]–[51].In this thesis, optically active epitaxially–grown semiconductor quantum dotshave been studied in view of their integrability into future quantum networks.The main focus of the thesis has been quantum optics experiments with twotypes of quantum dots emitting in the telecom range carried out with InAsPnanowire quantum dots and InAs/GaAs quantum dots. The InAsP nanowiresquantum dots’ emission wavelength is shifted from the near–infrared (NIR) allthe way up to the telecom range, covering both telecom bands. The emission ofthese quantum dots and the required growth processes for shifting the emissionwavelength are discussed in Paper 2. Single photon emission (see Section 8.1) isdemonstrated. InAs/GaAs quantum dots emitting in the telecom C–band areintegrated onto a piezoelectric substrate (see Section 5.2) in order to reversiblytune the emission wavelength, which is presented in Paper 3. We discuss amethod for integrating quantum dots independently of the growth process ontopiezoelectric substrates and demonstrate the emission of single and cascadedphotons. In Paper 5 single photons generated by an InAs/GaAs quantum dotare modulated into tunable sidebands using a phase modulator. We demon-strate that the modulation process leaves the single photon purity unaltered.In Paper 8 we employ two–photon resonant excitation (see Section 7.3 for adiscussion of excitation schemes) to generate pure single photons on–demand.

1. Introduction 3

Furthermore, we use a phonon–assisted resonant excitation scheme to generatehighly entangled photons on–demand. A discussion of generating and measuringentangled photon pairs is found in Section 2.4 and 8.3.Also quantum dots with emission outside of the telecom range are studied,namely droplet–etched GaAs quantum dots that emit close to the D1–transitionin Rubidium. Quantum memories based on atomic transitions (e.g. in Rubid-ium) could be used for storage of quantum dot photons, hence it is beneficial todevelop quantum dots with emission in the vicinity of these transitions.In Paper 1, we demonstrate single photons with unrivaled purity generatedby a quantum dot under two–photon resonant excitation. Resonance fluores-cence (see Section 7.3) is used to generate highly indistinguishable photonson–demand without the need for Purcell enhancement, which is summarizedin Paper 4. We integrate GaAs quantum dots into piezo-tunable broadbandparabolic microcavities to enhance their extraction efficiency. The structure de-sign is investigated in finite difference time domain simulations and on–demandsingle photon emission is generated via two–photon resonant excitation froma fabricated device. The results are presented in Paper 7. Highly entangledand indistinguishable photons are generated on–demand from a GaAs quantumdot and we demonstrate entanglement swapping with these photons in Paper 6.Finally, we study the limitations of resonance fluorescence versus two–photonresonant excitation in view of simultaneously generating highly indistinguishableand pure single photons in both theory and experiment which is presented inPaper 9.

4 1. Introduction

Thesis structure.In Part I, I discuss the theoretical background and experimental methods re-quired for the publications in Part II.Chapter 2 contains the fundamentals of photon statistics which are relevant todistinguish quantum states of light from thermal and coherent light. Also, theconcepts of two–photon interference and entanglement are introduced.In Chapter 3, I touch upon emitters of single and entangled photons in thetelecom range. After giving a broad overview of available sources of quantumstates of light, I focus on epitaxially grown optically active semiconductorquantum dots, which are the emitters studied in this thesis. This includes theelectronic properties, available material systems and finally a recap of recentdevelopments of quantum dots in the telecom range.Photonic structures that are used enhance the extraction efficiency of semicon-ductor quantum dots are discussed in Chapter 4, where I differentiate betweenstructures that provide a cavity effect and structures that act as waveguides.Finally an overview over micostructures in the telecom range is given.In Chapter 5, techniques for tuning quantum dots’ emission wavelength andfinestructure splitting are reviewed with a focus on strain tuning.Chapter 6 introduces the three different types of quantum dots that have beenstudied during this thesis work including sample growth and processing.Having laid a theoretical background, experimental methods are discussed start-ing in Chapter 7. Here, I introduce micro–photoluminescence measurementsand the basic setup design used in the experiments presented in Part II. Also ,characterization methods are discussed. The chapter is concluded by reviewingnon–resonant and resonant optical excitation techniques.The experimental principles of correlation–spectroscopy are disclosed in Chap-ter 8. Here, I discuss auto–correlation (Hanbury Brown and Twiss), two–photoninterference (Hong–Ou-Mandel) and polarization resolved cross–correlation mea-surements. This includes methods for data analysis.In the appendix, I discuss how we have implemented narrow–band and highlyefficient spectral filtering with a homebuilt transmission spectrometer in Chap-ter A. In Chapter B, I present our results on reducing the finestructure splittingin InAs/GaAs quantum dots in the telecom C–band via adjusting the quantumdot growth temperature. Chapter C touches on the fiber network that ourresearch group is setting up together with Ericsson Research Lab in Stockholmand summarizes fiber properties and some first measurements.

Chapter 2

Photon statistics

Photon statistics characterizes different types of light in terms of intensityfluctuations and allows to determine whether photons emitted from an emitterexhibit quantum properties. In the following, I will discuss the theory of photonstatistics and the second–order coherence that mathematically describes theintensity fluctuations of a light source. Furthermore, two–photon interferenceand the applications of indistinguishable photons, as well as the concept ofentanglement are discussed.

2.1. Types of lightPhoton statistics measurement are a tool to distinguish between different types oflight, in particular classical states of light (thermal light and coherent light) andnon-classical states of light (photon–number or Fock–states). In the following,the probability distribution P (n) and the variance (Δn)2 ≡ 〈n2〉 − 〈n〉2 of eachof the types of light will be used for their classification. Thermal light, emittede.g. by a light bulb, is characterized by intensity fluctuations at least on thesame order of magnitude as the mean photon number. The probability for

Photon number n

0 10 20 30 40 50

Pro

babi

lity

P(n

)

0.05

0

0.1

0.15

Photon number n

0 10 20 30 40 50

0.05

0

0.1

0.15

Photon number n

0 10 20 30 40 500

0.5

1.0

(a) (b) (c)

Figure 2.1: Probability distribution to find n photons for a mean photon numberof 〈n〉 = 7 for (a) thermal light, (b) Poissonian light and (c) a photon numberstate.

5

6 2. Photon statistics

finding n photons in a mode for a mean photon number 〈n〉 is given by:

Pth =〈n〉n

(〈n〉+ 1)n+1 . (2.1)

The variance is (Δn)2 = 〈n〉2 + 〈n〉. This type of distribution exhibits amaximum probability at n = 0, independent of the mean photon number 〈n〉,which is shown in Figure 2.1 (a).Coherent light which is emitted e.g. by a laser can be described with so–calledGlauber states in the second quantization notation [52]:

ai |αi〉 = αi |αi〉 (2.2)

|αi〉 =∑

n|n〉〈n|αi〉

=∑

nexp

(−1

2|αi|2

)αn

i√n!

|n〉 (2.3)

These states of light yield a probability distribution following Poisson statistics,describing emission events that are temporally completely unrelated:

Pcoh(n) = exp(−|αi|2

) |αi|2n

n! (2.4)

Pcoh(n, 〈n〉) = exp (−〈n〉) 〈n〉n

n! (2.5)

Here, the probability distribution peaks around the mean photon number, shownin Figure 2.1 (b). With equation 2.2 we find that the variance (Δn)2 is equalto the mean photon number 〈n〉.Photon number states or Fock states emerge from field quantization. Here, niphotons are in the mode i, with the Fock state |ni〉 being the eigenstate of thephoton number operator ni:

ni ≡ a†i ai (2.6)

ni |ni〉 = a†i ai |ni〉= ni |ni〉 (2.7)

These states of light are mutually orthogonal, hence:

〈ni|mi〉 = δnm. (2.8)

The probability distribution to find n photons in mode i is:

PFock(n) ={

1 : n = ni0 : n �= ni

(2.9)

The expectation value 〈n〉 of a state n is the eigenvalue of that state, whichleads to a vanishing variance. This is graphically depicted in Figure 2.1 (c).

2.2. Second–order coherence 7

2.2. Second–order coherenceThe difference between these classes of light lies in the statistics in respect of themean photon number. Mathematically this is characterized by the second–ordercoherence function g(2)(τ) at two points t and τ in time:

g(2)class(t, τ) =〈I(t)I(t + τ)〉

〈I(t)〉2

=〈E∗(t)E∗(t + τ)E(t)E(t + τ)〉

〈E∗(t)E(t)〉 , (2.10)

with I(t) the intensity of the light and E(t) the field intensity and 〈...〉 indicatingtemporal averaging. For a more general description, a quantum mechanicalnomenclature can be used in which creation (a†k) and annihilation operators(ak) for photons in the mode k are employed. Following the second quantizationas discussed in Ref. [53], the radiation field can be expressed in the followingway that includes the creation and annihilation operators:

Ek(t) = E(+)

k (t) + E(−)

k (t) (2.11)

E(+)

k (t) ∝ ak · exp(−i

(ωkt − �k�r

))(2.12)

E(−)

k (t) ∝ a†k · exp(+i

(ωkt − �k�r

))(2.13)

Using these relations and equation 2.10, we obtain the general description ofthe second–order coherence function:

g(2)QM(τ) =〈E(−)

k (t)E(−)

k (t+ τ)E(+)

k (t+ τ)E(+)

k (t)〉〈E(−)

k (t)E(+)

k (t)〉2(2.14)

=〈a†ka†kakak〉〈a†kak〉2

. (2.15)

To yield equation 2.15 from 2.14, we have used the commutator relation forbosons

[aj,εj , a

†k,εk

]= δjkδεjεk and τ → 0. Finally, we obtain

g(2)QM(0) =〈n(n − 1)〉

〈n〉2 (2.16)

=〈n2〉 − 〈n〉

〈n〉2 . (2.17)

In order to distinguish the different types of light that were introduced in theprevious section, we can now substitute the variance (Δn)2 ≡ 〈n2〉 − 〈n〉2 inequation 2.17 and use the variances obtained for thermal light, coherent lightand the photon number states. The resulting second–order coherence functionsat zero time delay are summarized in table 2.1. For thermal light a bunchingis observed, meaning that if a photon at time t is detected, it is very likelythat another photon is detected immediately after. For coherent light, the


Type variance (Δn)2 g(2)(0) commentthermal 〈n2〉+ 〈n〉 2 bunchingcoherent 〈n〉 1 no correlationPhoton-number 0 1− 1

n antibunching

Table 2.1: Summary of variances and second–order coherence functions forthermal light, coherent light and photon number states.

photons are completely uncorrelated, whereas for photon number states so–called antibunching is observed. For one ideal single photon source (n = 1), thesecond–order coherence function yields g(2)(0) = 0. For single photon sourcessuch as semiconductor quantum dots (see also Section 3.3) which emit photonsfrom a distinct transition between an excited state and the ground state, thenext photon can only be emitted after re–population of the excited state. Hence,the emission from this transition is blocked until the next excitation process.If n emitters of single photons are studied at the same time, the second–ordercoherence function will yield values of 1− 1

n at τ = 0 and is, thus, also a toolto estimate the number of contributing emitters.

2.3. Two–photon interferenceIndistinguishable photons are a resource in linear optical quantum computing [9],entanglement swapping [54] and quantum teleportation [55]. They find applica-tions in long distance quantum key distribution [13]–[15], large scale quantumnetworks [28] and quantum sensing with NOON-states [4], [56], [57]. In theseapplications indistinguishable photons interfere on a beam splitter which actsas an entangling gate. Indistinguishable photons are characterized by exhibitingthe same properties in terms of wavelength, polarization, and their wavepacketsare the same in terms of spectral and temporal shape. Experimentally the indis-

(a) (b) (c) (d)

A

C

B

D

Figure 2.2: Exit possibilities at beam splitter outputs C and D that photonscan take when incidenting on the two inputs A and B. (a) Photon A is reflectedand photon B is transmitted. (b) Transmission of both photons. (c) Reflectionof both photons. (d) Photon A is transmitted and photon B is reflected.

tinguishability of photons is quantified by interfering them on a non–polarizing

2.4. Entanglement 9

beam splitter in a Hong–Ou–Mandel style experiment [58]. Let’s consider aloss–less 50:50 beam splitter with two input (A and B) and two output ports(C and D). Furthermore, we consider the annihilation and creation operatorswith a† |n〉a =

√n + 1 |n + 1〉a, as previously introduced for photon number

states, and their bosonic commutator relations [a†, b†] = a†b

† − b†a† = 0. The

transfer of the operators between two modes a† and b†

at the input ports andtwo modes c† and d

†at the output ports of the beam splitter can be described

in a matrix formalism following the quantum mechanical description of thebeam splitter [59]: (

a†

b†

)=

1√2

(1 11 −1

)(c†

d†

)(2.18)

The incoming and outgoing state of the two indistinguishable photons on thethe beam splitter can then be described as follows:

|Ψin〉 = a†b† |0〉a |0〉b (2.19)

= |1〉a |1〉b (2.20)

|Ψout〉 = 1

2

(c† + d

†)(c† − d

†) |0〉c |0〉d

=1

2

(c†c† − d

†d†) |0〉c |0〉d

=1

2(|2〉c |0〉d − |0〉c |2〉d) (2.21)

Based on their bosonic nature two indistinguishable photons that are interferedvia the two input ports of a beam splitter will exit the beam splitter either bothat output port C or both a output port D (behaviors shown in Figure 2.2 (a)and (d)). For distinguishable photons, all options shown in Figure 2.2 will takeplace with the same probability.

2.4. EntanglementThe notion of entanglement came up in the 1930s when Einstein, Podolskyand Rosen suggested a Gedankenexperiment to disprove quantum theory [60].In the experiment a particle is decaying into two particles with equal massand opposite momenta. An experimentalist who measures the momentum ofone of the particles would instantaneously also know the momentum of thesecond particle. It has to be noted that the momenta of the particles are aproperty of their joint state and not defined before the measurement is taken.This is even the case if the particles are arbitrarily far away, thus, Einsteinalso referred to this as ’spooky action at a distance’ [61]. This purely quantummechanical concept is still fascinating and the existence of entanglement hasbeen experimentally verified in a variety of experiments. The term entanglementwas coined by Schrodinger in 1935 [62] and describes a quantum state that isno longer factorisable but can only be described as a whole. Einstein, Podolsky


and Rosen suggested the existence of hidden variables to complete - the intheir understanding incomplete - quantum theory. In 1964 Bell published apaper with a proposal to measure correlations between the two particles whoseoutcome should disagree with the statistics of quantum mechanics. In thepaper he introduced the so–called Bell’s inequality, a violation of which woulddisprove the existence of hidden variables. His proposal should violate theso–called Bell’s inequality that he introduced in the paper and, thus, disprovethe existence of hidden variables [63]. First experimental demonstrations werepresented by Freedman and Clauser [37] with preparatory work by Kocher [36],and Aspect [64], recently loophole–free Bell tests have been performed [65], [66].Today, entanglement is used as a resource in quantum information, e.g. forsecure key distribution [14], [15], [25], quantum metrology [3], [4], [67], [68]and quantum communication (over long distances) [29], [69]. Consideringlong distance applications, photons as flying quantum bits are the informationcarrier of choice. In semiconductor quantum dots the emission of polarizationentangled photons has been proposed to occur via the biexciton–exciton cascade(see Section 3.3.1 for more detail) in 2000 by Benson [70]. As described inSection 3.3 the photons emitted via the radiative cascade form the Bell stateΨ+:

Ψ+ =1√2(|HH〉+ |VV〉) (2.22)

which is a maximally entangled two–photon state. Entangled photon emissionfrom a quantum dot was first experimentally demonstrated in 2006 [44] witha fidelity of 70% to Ψ+. The level of entanglement can be characterized forexample by the fidelity, which describes how close the measured quantum stateis to a known maximally entangled state. Here, a fidelity of 100% correspondsto a perfect overlap of the two states, a fidelity larger than 50% is the lowerlimit to qualify a state as entangled, 0% corresponds to two orthogonal states.The fidelity can be estimated via 6 measurements, making it an accessibleparameter:

f =1

4(1 + CH + CD − CC) , (2.23)

with the Ci representing the fraction of cross–polarized light in the rectilinear(H), diagonal (D) and circular (C) basis

Ci =g(2)‖ (τ)− g(2)⊥ (τ)

g(2)‖ (τ) + g(2)⊥ (τ). (2.24)

Here, the subscripts ‖ and ⊥ refer to parallel polarization for biexciton andexciton (e.g. HH measurement), and cross–polarized measurement (e.g. HVmeasurement), respectively. Since the fidelity is measured by comparing to aspecific state, phase shifts introduced by birefringent elements of the experimen-tal setup can degrade the observed fidelity without destroying the entanglement.On the other hand, the oscillations between the two Bell states, which canbe observed for some quantum dots (see Sections 3.3.1 and 8.3), can only be

2.4. Entanglement 11

observed for such a phase–sensitive quantity. Another measure to characterizethe entanglement is the so–called concurrence, which also takes values between0% to 100%. The concurrence is not sensitive to introduced phases and alsoindependent of the reference frame, however can only be obtained via the den-sity matrix ρ, which requires at least 16, but ideally 36 polarization resolvedmeasurements. The concurrence is defined in the following way [71]:

C(ρ) = max (0, λ1 − λ2 − λ3 − λ4) , (2.25)with the λi being the eigenvalues (in decreasing order) of the matrix R:

R = (√ρρ

√ρ)

12 (2.26)

with ρ = (σy ⊗ σy)ρ∗(σy ⊗ σy) (2.27)

and σy =

(0 −ii 0

). (2.28)

Since 2006, improvements have been made in terms of resonant excitationschemes and also in terms of time resolution of the used detectors. By the timeof writing, the highest fidelity to the Bell state Ψ+ achieved with photons froma quantum dot is (98.7± 0.6)%, with a concurrence of (98± 1)% [72].

Chapter 3

Sources of single and entangled photons attelecom wavelengths

Fiber–based communication is carried out mainly within wavelength rangesthat exhibit lowest transmission loss in optical fibers. Most prominently theseare the so–called telecom O–band (for original band) located between 1260 nmto 1360 nm with transmission losses of approximately 0.6 dBkm−1 and thetelecom C–band (for conventional band) located between 1530 nm to 1565 nmwith transmission losses as low as 0.2 dBkm−1. While the losses in the O–bandare comparatively higher, the band is still used in some cases as it exhibits adispersion minimum resulting in minimal signal distortion due to chromaticeffects.This chapter deals with sources of single and entangled photons at telecomwavelengths. I discuss the basic principle of several generation processes andmaterial systems along with some historic and state–of–the–art results of therespective sources. This includes photons generated via spontaneous processes,defects and Carbon nanotubes and finally epitaxially grown optically activesemiconductor quantum dots. Since quantum dots are the sources employed in allworks presented in Part II of this thesis, their electronic and consequent opticalproperties are discussed in depth. The chapter is concluded by an overviewover the historic developments of semiconductor quantum dots emitting in thetelecom range and a collection of experimental results performed with telecomquantum dots.

3.1. Spontaneous conversion and mixing processesPhotons generated via spontaneous processes, e.g. spontaneous parametric downconversion (SPDC) or four–wave mixing (FWM) have historically been theworkhorse for quantum optics experiments in the telecom range. The generationof entangled photon pairs via a type–II–SPDC crystal was first demonstratedby Kwiat et al. [73] in the near–infrared and a few years later by Brendel etal. at telecom wavelengths (1310 nm) [74] with techniques established in earlierwork [75]. In these down conversion processes a laser pump photon is convertedvia a non–linear effect into a signal and an idler photon, which are cross polar-ized in the case of so–called type–II–crystals. Energy and momentum of thepump photons are conserved in the process. Commonly, non–linear crystals

12

3.1. Spontaneous conversion and mixing processes 13

like Beta Barium Oxide (BBO) [73] and periodically poled potassium titanylphosphate (PPKTP) crystals [35] are employed for spontaneous parametricdown conversion. As the name suggests, the conversion is process is spontaneous,which results in an uncertainty of the photon generation time. Moreover, dueto the thermal photon statistics of the emitted photons, there is a trade–offbetween pump power and efficiency, that usually dictates to use low excitationpowers in order to avoid multi–pair generation. This in turn has a detrimentaleffect on the number of generated photon pairs. In a recent work on 12–photonentanglement [76] the photon pair generation probability had to be kept to0.05 to keep the rate of unwanted multi–pair generations as low as possible.For the observation of coincidences between 12 pairs this resulted in a rate of1 h−1, demonstrating the problematic nature of the efficiency–purity trade–offfor applications that demand high rates. Recent developments to overcome thisissue for heralded single photon sources have been made by Kaneda et al. [35]by implementing a time multiplexed scheme that stores one photon of the pairin an adjustable delay line upon the detection of the heralded photon. In thismultiplexing scheme with up to 40 modes the authors could show a collectionefficiency of up to 66.7% for a single photon. This corresponds to an almost10 fold increase compared to a non–multiplexed heralded single photon source.Photon pairs generated by SPDC have for example been used to demonstrateentanglement distribution in a deployed fiber under the Mediterranean betweenthe islands of Malta and Sicily (≈ 90 km) by Wengerowsky et al. [24] showingpolarization visibilities of 90%. Beyond this, demonstrations of quantum keydistribution in free–space have been performed over 144 km between the islandsof La Palma and Teneriffe [69] or over 1120 km connecting two ground stationsvia a satellite [25].Besides the commonly used crystals BBO and PPKTP, spontaneous conversionprocesses are observed in other material platforms like AlGaAs and Silicon.Both of these materials are heavily studied in terms of on–chip photonics anddevices. Polarization entangled photons in AlGaAs waveguides have been gener-ated by SPDC by Orieux et al. [77] at 1518 nm with a fidelity of 0.83 to the Bellstate |Ψ+〉 by using a counter–propagating phase matching technique. AlGaAswaveguides can be operated at room temperature and these sources could beminiaturized further by integrating the pump laser on chip. Shortly after thisfirst demonstration Valles et al. demonstrated the emission of entangled photonpairs in the telecom C–band from an AlGaAs waveguide using a different phasematching technique [78].In Silicon waveguides the generation of entangled photon pairs was first demon-strated by Takesue et al. [79] with emission wavelengths around 1.5μm basedon spontaneous FWM. In FWM two frequencies that interact in a non–linearmedium can generate two new frequencies within the constraint of energyconservation. Space–efficient micro–resonators like coupled resonator opticalwaveguides [80] and micro–ring resonators [81] have been investigated to gener-ate entangled photon pairs in and around the telecom C–band.For a detailed overview of semiconductor–based sources of entangled photon

14 3. Sources of single and entangled photons at telecom wavelengths

pairs, I suggest to the interested reader to study the following review paper byOrieux et al. [82].

3.2. Other sourcesEndo et al. presented near–telecom band emission from single wall Carbonnanotubes with emission around 1240 nm and autocorrelation measurementswith g(2)(0) = 0.6 at cryogenic temperatures and room temperature. Thelinewidth of these emitters is on the order of a few meV [83]. More recently,emission from defects in single wall Carbon nanotubes with emission in thetelecom O–band or C–band depending on the defect type that yield convincingantibunching at room temperature with g(2)(0) = 0.01 was presented [84]. Thedecay times are short (100 ps to 500 ps), however the brightness appears to below according to correlation measurements for both types of Carbon nanotubesemitters discussed here.Emission within the telecom bands has also been shown by Christle et al. fromvacancies in Silicon Carbide. Here, neutral and di–vacancy defects in a 4H–SiCmembrane have been generated by electron irradiation and emit between 1.1μmto 1.6μm. They yield g(2)(0) < 0.5 with long spin coherence times of ≈1ms[85], which could also be relevant for quantum sensing applications and spin–photon entanglement generation [29]. Single photon emission in the telecomrange (mostly O–band) was observed additionally by Wang et al. from cubicSilicon carbide films both at cryogenic temperatures and room temperature.Antibunching with a g(2)(0) = 0.13 is observed, as well as broad linewidths onthe order of 100meV [86]. The same research group also demonstrated thatnitrogen vacancies can be deterministically generated in Silicon Carbide filmsvia electron beam irradiation [87] which emit below and within the telecomO–band and emit single photons with g(2)(0) = 0.25. Also long spin coherencetimes of 17.1μs are found. Vanadium dopants in SiC have recently been shownto emit in the telecom O–band with optical lifetimes between 10 ns to 170 nsand a g(2)(0) = 0.1 [88].Erbium ions have been know to exhibit optical transitions in the telecom C–band, however with very long lifetimes on the order of milliseconds in the bulk.To overcome this obstacle for emission of telecom photons at high rates, Diboset al. have created Silicon photonic crystal cavities (see Section 4.1) close toEr dopants in an Yttrium orthosilicate crystal such that the Erbium ions canevanescently couple to the photonic crystal. This lead to a drastic decrease of thedecay time to 17μs and made the observation of single photon emission from theErbium ions possible with a g(2)(0) = 0.055 [89]. While the emitters presentedin this section show emission that is spectrally broad compared to atomicresonances, the room temperature emission and the potential integrability ofCarbon nanotubes and Silicon Carbide membranes is of interest for hybridquantum systems and long spin coherence times could be relevant for thegeneration of spin–photon entanglement [90], [91].With regard to more complex quantum systems that also include quantummemories, Rubidium atoms are of interest both for photon generation and

3.3. Optically active epitaxial semiconductor quantum dots 15

storage. Warm Rubidium vapor can emit pairs of photons with one photon inthe near–infrared (780 nm) and the other one at telecom wavelengths (1377 nm)by spontaneous FWM. The photons are entangled [92] and the system can alsobe used as a heralded single photon source with a g(2)(0) = 0.06.

3.3. Optically active epitaxial semiconductor quantum dotsQuantum dots are nanostructures consisting of some 103 − 105 atoms andrepresent a confinement potential for charge carriers. In the following, the termquantum dots will denote optically active epitaxial semiconductor quantum dots,as opposed to colloidal quantum dots or electrostatically defined quantum dots,which are both not part of this thesis. More specifically, all studied quantumdots are III–V–semiconductor quantum dots in semiconductor heterostructures.The charge carrier confinement is generated by encapsulating a semiconductormaterial with smaller bandgap in a material with comparatively larger bandgap.For confinement of charge carriers to occur, the wavefunctions of the chargecarriers has to be spatially restricted. In quantum dots, the wavefunctions areconfined in all three spatial dimensions, creating a zero–dimensional density ofstates. The density of states describes the number of states that are availableat a specific energy, for three–dimensional confinement the density of statesbecomes quantized. Therefore, only discrete energy levels can be occupied. Dueto their discrete energy spectrum, quantum dots are commonly referred to asartificial atoms. For the confinement to affect the density of states and, thus,the charge carriers, the size of the confined semiconductor has to be on theorder of the De-Broglie wavelength λDB

e,h , which is given by [93]:

λDBe,h =

h√3m∗

e,hkBT. (3.1)

Here, h is the Planck’s constant, m∗e,h the effective mass of either electron or hole,

kB Boltzmann’s constant and T the temperature. At low temperatures λDBe,h is

on the order of 10 nm to 100 nm. If the temperature is low enough, such thatkBT is smaller than the electron–hole binding energy mediated via the Coulombinteraction, electrons and holes can bind into quasi–particles called excitons.These quasi–particles can recombine radiatively via the emission of a photon.The details of generating excitons and other states in quantum dots via opticalexcitation are discussed in Chapter 7. In order to describe the energy spectrumin a quantum dot, it can be treated as an infinitely deep three–dimensionalpotential well with confining lengths Lx,y,z. Here, the possible eigenenergies areas follows:

E(�k) = �2�k

2

2m∗ (3.2)

=�2

2m∗∑

i=x,y,z

(π2ni

Li

), (3.3)


with ni being integer numbers. From this very simple approximation, we canalready conclude that the energy spectrum is dependent on the effective massand, thus, the semiconductor material and it is also inversely proportional to theconfining lengths. In other words, smaller quantum dots of the same materialemit at higher energies or shorter wavelengths. This description is howevertoo simplified for realistic quantum dots which are typically lens-shaped withhigh aspect ratios. The high aspect ratio leads to the confinement in growth(z-) direction being stronger than the in–plane (x-, y-) confinement, hencesmall energetic distances between the in–plane energy levels. For the in–planeconfinement, a slowly varying wavefunction can be assumed, which allows toseparate the in–plane components from the component in growth direction [94],[95]. Due to the comparatively larger energetic splitting along the z–direction,only the lowest energetic state is considered in this direction. With theseapproximations, we arrive at a two dimensional harmonic oscillator describingthe parabolic confinement in the lateral directions:

H =�p2

2m∗e,h

+m∗

e,hω20

2

(x2 + y2

). (3.4)

By solving the Schrodinger equation, the following eigenenergies are obtained [96],[97] for a quantum dot with circular in–plane symmetry:

En,l = �ω0 (2n + |l|+ 1) = �ω0(s + 1), (3.5)

with the principal quantum number n = 0, 1, 2, ..., and the azimuthal quantumnumber l = ±0,±1, .... s is referred to as the shell index with s = 2n + |l|.Analogously to atoms, the shells are labeled s-, p-, d-, ... shell with increasing s,with a degeneracy of 2(s+1) for each shell. The relaxation of charge carriersinto the s–shell is fast after the excitation process, thus, in this thesis we onlyconsider emission from the s–shell. As mentioned earlier, emission from aquantum dot is the bright recombination of an exciton. This process has tofollow dipole selection rules ΔMJ = 0,±1. Here, M is the angular momentumprojection of the excitonic states. J is the total angular momentum J = L ±S, consisting of the angular momentum and the spin. For electrons, Le = 0and Se = 1

2 and for holes Lh = 1 and Sh = 12 , which results in three different

total angular momenta for heavy holes, light holes and split–off holes (heavyholes: Jhh = 3

2 with Jhh,z = ± 32 , light holes: Jlh = 3

2 with Jlh,z = ± 12 and

split–off holes: Jso = 12 with Jso,z = ± 1

2 ). For all quantum dots studied inthis thesis, only the heavy hole – electron states are considered, as they arethe lowest energy states exciton for the InAs/GaAs quantum dots [98]. In thedroplet etched quantum dots light hole and heavy hole mixing is below 5% forhighly symmetric quantum dots [99] and in the InP nanowire quantum dotsthe light hole emission does not couple to the waveguide (see Paper 2). Asmentioned above, the s–shell is two fold degenerate and can be at most occupiedby two electrons and two holes according to the Pauli principle. The possibleoccupations of the s–shell are illustrated in Figure 3.1 and can be pooled intofive possible configurations of which four are optically active. The bright exciton


(a) X (b) DX (c) X+ (d) X- (e) XX

Figure 3.1: Spin configurations of all possible states in the quantum dot s-shell.Dark blue circles and arrows represent electrons, light blue represents holes.The spin is indicated via the arrow direction. (a) Exciton. (b) Dark exciton.(c) Positively charged trion. (d) Negatively charged trion. (e) Biexciton.

(Fig. 3.1 (a)), consisting of one electron and one hole in two possible spinconfigurations. The dark exciton which is forbidden to decay optically activelydue to selection rules (Mdark = ±2, no photon with spin ±1 can be emitted),see Fig. 3.1 (b). Dark states were not investigated during this thesis, but arementioned for the sake of completeness. If an additional charge carrier is presentin the s–shell, a positively (X+) or negatively charged (X−) trion can decayradiatively. The binding energy EB with the additional charge shifts the energyof the trion states compared to the neutral exciton. The highest occupation ofthe s-shell with two electron hole pairs is the so–called biexciton XX (Fig. 3.1(e)). Compared to two single excitons, also for this state the emission energyis shifted via to the biexciton binding energy. Due to the additional Coulombterms compared to the neutral exciton, all these states decay with distinctemission energies, which is also discussed in more detail in Chapter 7.

3.3.1. Biexciton–exciton cascadeAs previously mentioned, a fully occupied quantum dot s–shell with two electronsand two holes is a so–called biexciton. The biexciton state decays to the groundstate via the exciton state. In this process, the decay of the so–called biexciton–exciton cascade two photons are emitted consecutively. The radiative cascade isa resource for generating pairs of polarization entangled photon pairs which hasbeen proposed in 2000 by Benson et al. [70] and has since then been studied innumerous experiments, for experimental details see also Section 8.3. In Figure3.1 the two exciton spin configurations have been indicated, however so far theexchange interaction between electrons and holes that can lift the energeticdegeneracy between the two bright exciton states has not been accounted for.The exchange interaction is described by the following Hamiltonian:

Hexc = −∑

i=x,y,z

(aiJh,iSe,i + biJ

3

h,iSe,i

). (3.6)

Here, ai and bi characterize the interaction strengths of the spins dependingon the confinement potential, and Jh,i and Se,i are operators of the respective


spins along the axis i. Following the extensive work of Bayer et al. on quantumdot finestructure splitting, the Hamiltonian can be expressed in a matrixrepresentation using the exciton eigenstates for bright |±1〉 and dark excitons|±2〉 [100]:

Hexc =1

2

⎛⎜⎜⎝δ0 δ1 0 0δ1 δ0 0 00 0 −δ0 δ20 0 δ2 −δ0

⎞⎟⎟⎠ , (3.7)

with δ0 = 1.5(az + 2.25bz), δ1 = 0.75(bx − by) and δ2 = 0.75(bx + by). Fromequation 3.7 it can be understood that the bright and dark exciton states donot mix (see the block–diagonal form) and are split by the factor δ0. Theoff–diagonal elements δ1 and δ2 account for the splitting of the bright and darkstates. For δ1 = 0, which would be the case for bx = by in quantum dots withrotational symmetry, the bright exciton states |+1〉 and |−1〉 are eigenstates ofHexc with eigenenergies 1

2δ0 and are not split. The symmetry is not only limitedto the quantum dot shape but also to composition due to alloying [101]. Ifδ1 �= 0, the eigenstates of the bright excitons are 1√

2(|+1〉 ± |−1〉) with energies

12 (δ0 ± δ1). The finestructure splitting is observed in both biexciton and excitonemission since the biexciton itself already decays into one of two non–degenerateexciton states. This is resulting in an observable energy difference betweenthe two biexciton states (unless in the case of Δ = 0μeV). However, it shouldbe noted that the biexciton itself does not exhibit a finestructure splitting asit is in a singlet state. This is also the case for the trion states [102]. Theconsequence of the finestructure splitting is illustrated in Fig. 3.2. In 3.2 (a)the energy levels of a quantum dot without finestructure splitting are shown.Here, the emitted photons from the biexction–exciton cascade are left and rightcircularly polarized with a respective cross–polarized emission of the subsequentexciton. The two exciton levels are degenerate in energy the two decay paths areindistinguishable, thus, they co–exist in a superposition, yielding the followingentangled state:

|Ψ〉 = 1√2(|RL〉+ |LR〉) (3.8)

=1√2(|HH〉+ |VV〉) (3.9)

In Figure 3.2 (b) the degeneracy between the exciton levels is lifted due to a finitefinestructure splitting Δ. This is making the two decay path distinguishablevia the energy of the emitted photons. In this case, the two–photon state is nolonger time–independent [103] and takes the following form:

|Ψ(t)〉 = 1√2

(|HH〉+ exp

iΔt�

|VV〉). (3.10)

A time dependent phase has now been introduced between the horizontal andvertical decay path, expressing that the exciton state is oscillating between the


X

XX

0

RXX

LX

XX X

Energy

Inte

nsit

y

RX

LXX

E

X

XX

0

VXX

VX

V V

Energy

Inte

nsit

y

HX

HXX

E

H H

EE(a) (b)

Figure 3.2: Biexciton–exciton cascade for (a) a quantum dot without finestruc-ture splitting and (b) a quantum dot with finestructure splitting (Δ �= 0μeV).The biexciton binding energy EB is marked as the difference between twice theexcitonic energy to the biexciton energy shifted by Coulomb interaction. Toppanel: cascaded level scheme. Bottom panel: schematic spectra.

two possible eigenstates once the biexciton photon has been emitted. In prac-tice, this leads to an oscillation between the two Bell states 1√

2(|HH〉+ |VV〉)

and 1√2(|HH〉 − |VV〉) depending on when the exciton photon is detected with

respect to the emission of the biexciton photon. It has been shown that theemitted photons of a quantum dot with finestructure splitting are still in amaximally entangled state [104], however the time resolution of the experimentalequipment must be good enough to resolve the oscillations with time constantτ = �

Δ .Typical sizes of the finestructure splitting for the different quantum dot typesused in this thesis are discussed in Chapter 6. Possibilities to reduce or removethe finestructure splitting have been investigated both for growth methods andpost–growth experimental techniques. This includes the growth of nanowirequantum dots as it has been predicted that only based on their symmetry thefinestructure splitting should vanish [105], the growth of droplet–etched GaAs


quantum dots in symmetric AlGaAs nanoholes [106]–[108] and the growth ofsymmetric GaAs quantum dots on (111) substrates via droplet epitaxy [109],[110]. Furthermore, thermal annealing [111]–[113], as well as the application ofexternal magnetic fields [100], electric fields [114]–[116], strain [117]–[122] andcombinations of electric field and strain [123] have been applied. A more com-prehensive discussion of quantum dot strain tuning can be found in Chapter 5.

3.3.2. Development of telecom quantum dotsCurrently, the most common material systems to grow quantum dots withemission at telecom wavelengths are InAsxP1−x quantum dots on an InP sub-strate or In1−xGaxAs quantum dots on a GaAs substrate. In this thesis bothInAsP quantum dots in InP nanowires and self–assembled InAs quantum dotson GaAs substrate with a metamorphic buffer layer were studied. In Figure 3.3an overview over semiconductor compounds that can exhibit emission in thetelecom bands is given, showing their lattice constants and bandgap energies.When quantum dots in the telecom range are grown, not only the band gapenergy of the compound or the ternary material determine the emission energyof the quantum dots. The strain introduced by lattice mismatch, the exactmaterial composition and also the quantum dot size are crucial parameters aswell. When different semiconductor compounds are epitaxially grown on oneanother, strain due to lattice mismatch can lead to the formation of quantumdots [124]. For InAs on GaAs the lattice mismatch is quite large (≈ 7%) and isgenerating strained quantum dots that emit from an effectively increased bandgap at around 900 nm to 950 nm [125]. In order to grow quantum dots withemission shifted towards the telecom ranges, several measures can be taken.These include:Increasing the quantum dot size which is e. g. achieved by epitaxially growingthe quantum dot layer while alternating the flux of InAs and GaAs. Due toan increased surface migration, the quantum dot size is increased [127], [128].Another option to increase the quantum dot size is to stack the quantum dotlayer on top of a buried seed quantum dot layer, which results in less strainedand larger dots in the stacked layer [129], [130]. By epitaxially capping thequantum dots with a GaAs layer [131] at low growth temperatures, an inter-mixing between Indium and Gallium can be reduced, as well as an Indiumdesorption, which helps maintaining the quantum dots size.Capping with strain reducing layers that contain Indium preserves the Indiumconcentration in the quantum dot during growth. Thus, the quantum dot size isnot only increased, but also the strain to the final GaAs capping layer is reducedand quantum dot emission around 1300 nm [132], [133] and even 1.5μm [134]can be observed. Also approaches that combine strain reducing layers withstacked quantum dot growth have been explored to achieve emission at andbeyond 1.55μm [135].Growing quantum dots on a metamorphic buffer layer (MMBL) allows to gradu-ally increase the lattice constant within a micrometer sized layer by continuouslyincreasing the Indium content in an In1−xGaxAs–layer. The quantum dots are


Lattice constant (Å)

5.6 5.7 5.8 5.9 6.0 6.1

Ban

dgap

ene

rgy

(eV

)

0

0.5

1.0

1.5

2.0

2.5

Em

issi

on w

avel

engt

h (

m)

AlAs

GaAs InP

GaSb

InAs

0.5

0.75

1.0

2.0

1.311.55

directindirect

O-band

C-band

Figure 3.3: Bandgap energy versus lattice constant of various semiconductorcompounds associated with emission at telecom wavelengths at room tem-perature. GaAs and InP are the most common substrates for InAsxP1−x orIn1−xGaxAs quantum dots. AlAs and GaAs are quasi lattice-matched and canbe used to epitaxially grow DBR mirrors. The material constants are takenfrom [126].

grown on top of this strain–reduced interface compared to the substrate, whichis allowing emission within the telecom C–band on GaAs substrates [136]–[139].This concept is possible not only for In1−xGaxAs based MMBLs, but alsoAlGaAsSb MMBLs have been used for quantum dot–based lasers with emissionaround 1.55μm [140].InP substrates have a lower lattice mismatch of ≈ 3% to InAs. InAs/InPquantum dots have shown emission in the telecom C–band [141]. The majordrawbacks of this material system are the technological difficulty of growinghigh-refractive contrast and index lattice matched materials to generate DBRmirrors [142], [143] and the fragility of the wafers.To conclude this chapter, a lose overview of the developments of quantum dotsin the telecom range is given. Here, a few techniques are mentioned that will beexplained in detail in separate chapters of the thesis. For extraction efficiencyenhancing photonic structures, I refer to Chapter 4, for quantum dot tuningtechniques see Chapter 5, for quantum dot growth methods, see Chapter 6 and


for excitation methods Sections 7.3.1, 7.3.2 and 7.3.3. A timeline of selecteddevelopments for both quantum dots with emission in the near–infrared rangeand in the telecom range is presented in Figure 3.4. It can be observed thatdevelopments for telecom quantum dots have typically emerged later in time,which might be related to later developments in detector technology comparedto the detectors available for the near–infrared range. The first emission ofquantum dots at 1.3μm at room temperature was demonstrated by Mukai etal. in 1994 from an InAs/GaAs quantum dot ensemble [127] grown by metal–organic vapor–phase epitaxy (MOVPE). With the InAs/InP material systemthe first telecom emission between 1.4μm to 1.7μm was shown by Farfard et al.in 1996 [141]. The quantum dots had been grown by molecular beam epitaxy(MBE). At this point in time one of the main issues was to isolate single QDsfrom the ensemble because the quantum dot densities were high (on the order of1010 cm−2 [164]). This was overcome for example by etching mesa by Takemotoet al. [164] in 2004 which allowed to isolate single QD lines from InAs/InP dotsemitting from 1.3μm to 1.5μm at cryogenic temperatures. At this point thefirst direct overvation of exciton transitions in telecom QDs was demonstrated.In the same year, Ward et al. used InAs/GaAs QDs in small mesas that wereembedded in a p–i–n structure to perform the first electroluminescence of singleQDs close to 1.3μm [165]. In 2005 low density growth methods where beingdeveloped for example by Alloing et al. [166] for InAs/GaAs quantum dotsemitting at 1.3μm. An ultra–low growth rate was used to get the density to anorder of 2× 108 cm−2, corresponding to a quantum dot density of only 2μm−2.Ward et al. generated MBE–grown InAs/GaAs QDs within pillar microcavitiesemitting at 1.3μm from which they observed X and XX emission [125]. Thereduction of the quantum dot density allowed to isolate single quantum dot tran-sitions, enabling several groups to report the first autocorrelation measurementsperformed on quantum dots in the telecom range [125], [155], [156]. Soon after,these developments enabled the first decay time measurement by Zinoni et al.in 2006 [167] for InAs/GaAs quantum dots at 1.3μm, which revealed a decaytime of 1 ns for the biexciton. In the same year Cade et al. measured for thefirst time the finestructure splitting of their InAs/GaAs QDs, which was verylarge (250μeV) and studied the behavior of the QDs in a magnetic field [168].This is arguably the fist demonstration of tuning the emission wavelength attelecom wavelengths.Also the microstructure design for enhanced extraction efficiencies was progress-ing at the time: Yamaguchi et al. put their InAs/GaAs QDs into micropillarsand observed emission at 1240 nm with an enhancement in the emission ratesby a factor of two compared to the as–grown sample [169]. Miyazawa et al.employed tapered mesas to generate a more spatially directed emission [156].Takemoto et al. presented an optical horn antenna containing InAs/InP quan-tum dots which demonstrated in extraction of 11% into the first lens [170].The first pairs of entangled photons were experimentally demonstrated by Wardet al. in 2014 from an InAs/GaAs quantum dot with emission close to thetelecom O–band [157]. The QDs in the sample were embedded in a pin–structure


that allowed influence on the emission wavelength and the finestructure splitting.A time–dependent fidelity of up to 85% was presented. With a QD from thesame sample the authors showed interference between QD photons and laserphotons with a resulting visibility of 60% [171]. The emission of entangledphotons generated via continuous–wave non–resonant excitation in the telecomC–band was demonstrated by Olbrich et al. for an InAs/GaAs QD with afidelity of 61% [172] and by Muller et al. for an electrically–driven InAs/InPQD with emission in the S–band with a fidelity of 87% [173]. Two–photoninterference in the telecom O–band was demonstrated from consecutive QDphotons by Kim et al. [158] in 2016. In the experiment they used an InAs/InPQD integrated in a photonic crystal cavity yielding a raw visiblity of 18% anda corrected visibility of 67%.Compared with their near–infrared counterparts the QDs in the telecom rangeare slowly catching up and experiments performed with these long wavelengthsdots in the recent years show an increasing complexity going more and moretowards applications. To unleash their full potential QDs emitting in the telecomrange require integration in microstructures to further increase the extractionefficiency. Simultaneously, resonant excitation techniques are obligatory toobtain the ideal photon properties, as discussed in Section 7.3. Recent effortsin these directions are presented in the following.Resonant excitation techniques have been brought to application mostly inthe last 5 years. In 2016 Al–Kuhzheyri et al. used s–shell resonant excitationon an InAs/GaAs with emission in the telecom O–band which lead to theobservation of the Mollow–triplet at telecom wavelengths and near–transformlimited linewidths, which indicated little pure dephasing via this exciationmethod [174]. In 2019 Nawrath et al. performed continuous–wave and pulsedresonance fluorescence on InAs/GaAs quantum dots emitting in the telecomC–band. This lead to reduced linewidths compared to the above–band excita-tion case (reduced inhomogeneous broadening) and a state preparation fidelityof the excited state of 49.2%. The authors also performed continuous–wavetwo–photon excitation to generate indistinguishable photons with a fitted rawvisibility of 71.3%. Our work on two–photon excitation to generate on–demandsingle photons and phonon assisted two–photon excitation to generate entangledphotons on demand with a concurrence of 91.4% is presented in Paper 8.The generation of single and entangled photons from an InAs/InP quantum dotwith emission in the telecom C–band clocked with 1GHz has been demonstratedby Anderson et al. alongside with quantum teleportation of quantum dot pho-tons and laser photons with a postselected teleporation fidelity of 89% [160].With maturing quantum dot technology, first transmissions of quantum dotphotons in deployed fiber have been demonstrated by the Toshiba group inCambridge [175], [176]. The authors have transmitted entangled photons in thetelecom O–band with fidelities of above 90% across metropolitan scale distancesof 15 km to 20 km.Beyond the direct generation of quantum dot photons in the telecom range,another possibility is to perform quantum frequency conversion on photons


generated at different wavelengths (typically in the near–infrared) and down–convert the photons to telecom wavelengths. The concept of quantum frequencyconversion has first been introduced by Kumar [177] and is based on the sameconcept as regular frequency conversion, however at the single photon level.Quantum frequency conversion has been used by Zaske et al. to down–convertquantum dot photons from 711 nm to 1313 nm with an efficiency of 30% whileconserving the single photon nature of the quantum dot photons [178]. De Greveet al. have used quantum frequency conversion to down–convert quantum dotphotons from 910 nm to 1550 nm in order to observe spin–photon entanglement.In the experiment, conversion only took place if the NIR quantum dot photonsoverlapped with laser pump photons at 2.2μm within a window of 8 ps. Thiswindow in the energy domain is much larger than the energetic splitting betweenthe two decay paths and is, thus, removing the which–path information [90].Furthermore, quantum frequency conversion has been used to render photonsemitted at 900 nm by two remote quantum dots indistiguishable after frequencyconversion to the telecom C–band with a two–photon interference visibility of29% [179]. With frequency conversion also the temporal profile of the exponen-tial decay can be engineered, Rakher et al. showed a spectral conversion from1310 nm to 710 nm while changing the decay time from 1.5 ns to 350 ps [180]. Itis also worth mentioning that the process of frequency conversion is conservingthe polarization entanglement of the generated photons as well. Ramelow et al.showed this for up–converted photons that were originally generated via SPDC[181].


QD fabrication

Goldstein ‘85

PL of single QDs

Marzin, Fafard ‘94

Antibunching

Michler ‘00

HOM Santori ‘02

Entangled Photons

Young ‘06

HOM 2 QDs

Reindl ‘17

‘00

‘02

‘06

Quantum teleportation

Reindl ‘18

Boson sampling

Wang ‘17

‘18

‘94

‘04

‘95

‘05

‘14

‘16

‘20

QD emission at

1.3μm Mukai ‘94

QD emission at

1.55μm Fafard ‘96

Antibunching at

1.3μm Takemoto ‘04 Antibunching at

1.55μm Miyazawa

Entangled photons

at 1.3μm Ward ‘14

HOM Kim ‘16

HOM 2 QDs Kim ’16

NIR CCD: Boyle ‘70NIR SPAD: Cova ‘81NIR SSPD: Gol’tsmann ‘01

‘19

‘17

‘94

‘85

(a) (b)

Entanglement

swapping Basso Basset

& Zopf ‘19

Quantum teleportation

w\ laser Anderson ‘20

Telecom CCD: Rossi ’91Telecom SPAD: Townsend ’93Telecom SSPD: Pearlman ’05

t

Figure 3.4: Timeline of selected developments for (a) QDs emitting in theNIR. Achievements are summarized from References [43], [44], [110], [144]–[151].Publications of detectors for the NIR range have been added [152]–[154]. (b)QDs emitting in the telecom range. Achievements from the following referencesare summarized [127], [141], [155]–[160] including detector developments [161]–[163].

Chapter 4

Photonic structures for quantum dots

The epitaxially grown semiconductor quantum dots studied in this thesis arebased on III–V–semiconductor materials with high refractive indices, e.g. 3.4for GaAs for a wavelength of 1550 nm. Since the quantum dot emission ofunprocessed samples is typically isotropical, most of the emitted photons sufferfrom total internal reflection at the semiconductor air interface or are not evenemitted towards the collection optics. With conventional optical setups thisleads to a collection of less than 1% of the emitted photons [182]–[184]. Highefficiency sources of single and entangled photons are a requirement for scalablelong distance quantum key distribution, as the key rate and possible distributiondistance are fundamentally linked to the source brightness [51], [185]. Further-more, linear optical quantum computing [9], [186] has stringent requirements onthe efficiency of the sources used (efficiency >90% with g(2)(0) < 0.07) [187],as well as the detectors (efficiency >90%) to be able to operate without post-selection. In addition, also some quantum repeaters [188] require entangledphoton pair emission with efficiencies > 70% with a multiphoton probability< 10−4 [189]. To overcome this disparity between typical samples and requiredefficiencies, a variety of microstructures have been engineered and fabricatedaround quantum dots. Some of these structures have been previously mentionedin Chapters 3. In this chapter, a more general introduction to structures usedby the semiconductor quantum dot community will be given, including shortworking principles of the structures. This is followed by a discussion of extrac-tion efficiency efforts that have been undertaken for quantum dots emitting inthe telecom range. Finally, the structures used in this thesis will be discussed.A crude distinction can be made between structures that are generating awaveguiding effect that directs and guides the emission of the quantum dots andstructures that are based on cavity effects that not only enhance the direction-ality but also exhibit Purcell enhancement [190]. Microstructures that providea solely waveguiding effect are photonic wires like nanowires and photonictrumpets and lens–based structures including microlenses and solid immersionlenses (that exhibit not necessarily dimensions on the micrometer scale).

26

4.1. Microcavities 27

(a) (b) (c) (d)

(e) (f) (g)

Figure 4.1: Schematic illustration of common microstructures. Structures arenot drawn to scale. (a) Micropillar. (b) Photonic crystal cavity. (c) Microdisk.(d) Bull’s eye cavity (e) Photonic trumpet. (f) Nanowire quantum dot. (g)Mircolens.

4.1. MicrocavitiesMicrocavities such as micropillars [191]–[194], microdisks [43], [195] and pho-tonic crystal cavities [196]–[198], see also Figure 4.1, are based on a similarworking principle besides the structural difference. The cavity is modifying thespontaneous emission properties of the quantum dots inside the cavity via thePurcell effect [190]. If the quantum dot emission is on resonance with the cavitymode the quantum dot light field couples to the cavity mode and spontaneousemission into that mode is increased. How strongly the emission into the cavityis increased is characterized by the Purcell factor P, which is the ratio betweentransition rate of the free emitter and the emitter in the cavity. A Purcell factorof 1 would correspond to no effect on the enhancement, P < 1 to an inhibitionof the emission and a P > 1 to an emission enhancement. If the emitter is onresonance with the cavity, the Purcell factor is given by:

P =3

4π2

QV0

(λ

n

)3

, (4.1)

with the quality factor Q, the emitter wavelength λ, the refractive index nin the cavity and the modal volume V0. From this equation it can be seenthat large Purcell factors are provided by high quality factors or a small modevolume or a combination of both and results in an enhanced emission rate of

28 4. Photonic structures for quantum dots

the emitter based on a large number of available states in the cavity. The modevolume is often on the order of a few λ3 and the Q–factor can take values onthe order of 105 [199] Tuning the quantum dot into resonance with the cavityis typically achieved via temperature tuning [196], [200], electric field tuninghas also been explored [201], [202] to not reduce the indistinguishability ofthe photons [203]. Tuning techniques are discussed in more detail in Chapter5. The presence of Purcell enhancement for the on–resonance quantum dotoccurs in a reduced decay time of the emitted photons [192]. Quantum dotsin micropillars are amongst the most popular cavity structures with Purcellenhancement. The mirrors generate a confinement in the vertical direction,whereas the confinement in plane stems from total internal reflection on thesidewalls. In these structures, quantum dots are located within pairs of highreflective distributed Bragg reflectors with asymmetric reflector design to ensureemission in the forward direction. Quantum dots embedded in micropillarshave been used as sources of single and indistinguishable photons [147] andindistinguishable photons with high purity and brightness [204], [205]. Whilethese outstanding results have been achieved via resonant s–shell excitation andsubsequent filtering of the excitation laser via polarization suppression, thislimits the maximum available system efficiency. To overcome this limitation,micropillar cavities with elliptical profile have been studied [206], which due totheir asymmetric profile support two non–degenerate polarized cavity modes.The quantum dot can be tuned into resonance with one of the cavity modes orpolarizations, while the other spectrally separated mode can be used to excitethe quantum dot and, thus, generate polarized and highly indistinguishablephotons [206] with efficiencies of 60%. An alternative approach is based on acavity–waveguide device that uses s–shell resonant excitation along a waveguideperpendicular to the cavity, which made filtering obsolete [207].Photonic crystal cavities were first proposed by Yablonovitch and Sajeev in1987 [208], [209] and are based on the concept of a so–called photonic bandgapthat confines the light. Here, the bandgap is created by a periodicity in therefractive index that is on the order of the wavelength of the propagating light.This can e.g. be generated by introducing periodic holes via etching to modulatethe refractive index. Similar to a bandgap in a semiconductor that forms aforbidden range in terms of energy for electronic states, a photonic bandgapintroduces an energy range that does not allow propagation of photons. If afew holes are kept unetched, this produces a microcavity with can localize thelight in three dimensions. Photonic crystal cavities have shown to modify thequantum dots lifetime [198], [210], reached a strongly coupled state in the solidstate [196], generate indistinguishable photons [197], also with extraction effi-ciencies up to 44.3% [211]. Moreover, the generation of multi–photon entangledcluster states using a quantum dot in a photonic crystal cavity has recentlybeen demonstrated [212].Microdisk resonators support so–called whispering gallery modes that are guidedalong the circumference of the disk due to total internal reflection [213]. Aquantum dot in such a cavity was used to demonstrate the first single photon

4.2. Waveguiding structures 29

emission from a quantum dot in the year 2000 [43]. Quantum dots in microdiskshave been used to study cavity quantum electrodynamics [195], [200], [214],[215] to examine light–matter interaction.While cavities such as micropillars typically exhibit a narrowband enhance-ment, applications that rely on the generation of entangled photons from thebiexciton–exciton cascade (see also Section 2.4), two–photon resonant excitationschemes (see also Section 7.3.3) or multicolor excitation schemes require aspectrally broadband enhancement of the quantum dot emission or a broadbandtransmission, respectively. Circular Bragg gratings or bull’s eye cavities arephotonic structures that provide such an enhancement [216] and consist ofconcentric circular trenches with a not–trenched defect region in the center thatcontains the quantum dots. The periodic modulation of the refractive indexvia the concentric circular trenches of this structure is providing a photonicbandgap and therefore creates radial confinement. The ratio between upwardsand downwards emission is dependent on the depth of the trenches comparedto the total thickness of the structure (see supplementary of Ref. [217]). Outof plane confinement is provided via total internal reflection via under–etchingthe structure [216]–[218] or by adding a precisely spaced gold mirror below thestructure [219], [220]. Circular Bragg gratings can be designed to exhibit nearGaussian emission profiles [216], [217]. Very recently Liu et al. [219] and Wang etal. [220] both presented a highly efficient quantum dot source of indistiguishableand entangled photons with measured pair collection probabilities of 65% and62%, respectively.

4.2. Waveguiding structuresAs mentioned above, waveguiding structures do not exhibit Purcell enhancementand show a broadband enhanced extraction efficiency. Photonic nanowires areguiding quantum dot emission along their axial direction and can, with an opti-mized diameter, funnel the emission into their fundamental mode (HE11) [221],[222]. A conically tapered tip at the top of the nanowire is allowing the mode toadiabatically leak out of the nanowire while ascending which reduces scatteringof the photons and permitting efficient outcoupling [223]. The efficiency ofthe nanowires can be further increased by adding a bottom mirror that canreflect photons emitted away from the collecting optics back into the nanowiremode [224]. Nanowires can be fabricated both in top–down [221], [225] andbottom–up approaches [226], [227]. The etching process in the top–down ap-proach gives access to a wide range of tapering angles at the tip of the nanowire,enabling either conical or inverse conical tapers [225], [228].Photonic nanowires with inverse conical tapers are referred to as photonic trum-pets and have been designed with the objective of providing a guiding structurethat expands the mode into a Gaussian profile while being less susceptible tothe opening angle obtained in the top–down approach [228]. In these structuresthe quantum dots are placed very close to the base of the structure wherethe diameter is optimized for single–mode guidance of the fundamental mode.Extraction efficiencies into the first lens of 75% and overlaps with a Gaussian


mode of 58% have been demonstrated [228]. The flat top surface in combinationwith the Gaussian emission profile allows to attach these structures directlyto cores of optical fiber pigtails as demonstrated by Cadeddu et al. with acollection efficiency of 5.8% [229]. Such a device could not only be used as afiber–coupled source of single and entangled photons but also as a probe forsmall electric fields. Furthermore, photonic trumpets have also been used ashybrid opto–mechanical systems to study the interaction between phonons andexcitons [230], [231] and the effects of decoherence caused by phonons on photonindistiguishablility [232]. The concept of an ’hourglass’–shaped broadbandenhancing microstructure has been proposed recently, with a predicted couplingefficiency of 95% into a Gaussian profile [233], but is yet to see implementation.Unless a deterministic nanowire fabrication technique is used, the top–downapproach suffers from lower yields when working with self–assembled quantumdots. In bottom–up fabrication, the growth process is a combination of selective–area growth with vapor–liquid solid growth. A taper can be added to reduceback reflection and divergence of the photons leaving the top of the waveguidewhich facilitates efficient coupling to external optics [223]. Nanowire quantumdots have been predicted to exhibit a vanishing finestructure splitting based ontheir symmetry [105] and experimentally low splittings have been found on theorder of (3.4± 3.0) μeV [234]. The emission of polarization entangled photonpairs with fidelities >75% have been experimentally verified [234]–[237]. Fur-thermore, the photons emitted from the nanowire waveguide are in a Gaussianmode which is ideal for coupling the emitters to optical fibers. The multiphotonemission probability has been measured to be below 1% [238]. Considering theintegrability of the sources, nanowire quantum dots have been transferred andintegrated in photonic circuits on chip [239]–[241], demonstrating their potentialfor integrated hybrid quantum photonics.Another strategy to improve light extraction from the high index semiconductormaterial is with the use of lenses, either macroscopic solid immersion lenses(SILs) or etched or 3D printed microlenses. In either case, the idea is to reducethe high index contrast between the semiconductor sample and the air/vaccumin the cryostat and therefore to reduce total internal reflection. The curvedsurface helps to refract the emitted light rather upwards than sideways, whichincreases the extraction efficiency for a fixed numerical aperture of the collectingoptics.SILs [242] can be added to the sample after growth granted that the workingdistance of the used collection optics is large enough. The two most commongeometries are the hemispherical SIL and the superhemispherical (Weierstrass)SIL that can significantly increase the amount of extracted photons [243]. Thelarger the refractive index of the SIL, the larger the extraction efficiency fora given numerical aperture [182], [244]. Based on the smaller generated spotsize, the power density in the focal point is higher compared to not using a SIL,which can be beneficial for applications that are limited by available excitationpower or filtering magnitude. The use of a GaP hemispherical SIL with a silverbottom mirror yielded an extraction efficiency of 65% for single photons emitted

4.3. Extraction efficiency enhancement at telecom wavelengths 31

from GaAs quantum dots [184].The fabrication of microlenses by using deterministic methods allows to in-dividually enhance preselected quantum dots. Gschrey et al. demonstratedan extraction efficiency of 23% from a quantum dot in a Gaussian–shapedlens that was pre–characterized via cathodoluminescence and fabricated viain–situ electron beam lithography and subsequent dry etching [245]. By usingan optimized design with a metallic back mirror instead of a distributed Braggreflector an extraction efficiency of up to 85% is possible with such a structure(see Supplementary of Ref. [245]). The integration of single quantum dots with3D laser written structures has been demonstrated with both microlenses [246]and even micro–objectives [247]. This has led to an extraction efficiency en-hancement of a factor of 2 for the microlenses compared to the bare sample,while the objective has a measured extraction efficiency of 40%. Recently,more complex 3D printed lens geometries also in combination with direct fibercoupling have been demonstrated [248] with approximately 1% fiber couplingefficiency.

4.3. Extraction efficiency enhancement at telecomwavelengths

A variety of nano and micro–structures have been fabricated around quantumdots in the telecom range within the last decade. Mesas were used in theearly days of telecom quantum dots to isolate single quantum dots due togenerally high quantum dot densities. In the recent years there has beena trend towards more complex structures also for the telecom range, whichcan be accompanied by deterministically positioned structures that promisehigher extraction efficiencies compared to randomly positioned structures. Non–deterministically positioned structures that have been realized in the telecomrange include photonic crystal cavities with collection efficiencies of 36% by Kimet al. [158] and micropillar cavities with extraction efficiencies of up to 3.3%by Chen et al. [249]. Srinivasan et al. used quantum dots with emission in thetelecom O–band within a microdisk resonator to study strong coupling betweenthe emitter and the cavity [215]. Another integration of telecom quantum dotsinto cavities was presented by Kors et al., with quantum dots emitting in thetelecom S–band in photonic crystal cavities [250]. The authors observed anenhancement of approximately 40 for a quantum dot on resonance with thecavity mode.A combination of a high refractive index GaP solid immersion lens and a quantumdot membrane with backside gold coating was realized by Yang et al. and yieldeda brightness of 17% for InAs/GaAs quantum dots in the telecom O–band [251].Deterministically integrated InAs/GaAs quantum dots emitting in the telecom O–band were demonstrated by Sartison et al. using in–situ lithography to fabricateGaussian shaped microlenses via chemical wet etching with enhancement factorsof around 10 [252]. Srocka et al. used cathodoluminescence combined with in–sito E–beam lithography for deterministic selection of InGaAs/GaAs quantumdots in the telecom O–band [253]. The QDs were integrated into mesas which


yielded an extraction efficiency of 10%. The authors recently published anupdated structure with a gold backside mirror which operates at up to 40K [254].InAsP/InP nanowire quantum dots with emission in both telecom bands havebeen experimentally studied by Haffouz et al. and showed directional brightsingled photon emission with g(2)(0) = 0.02, which are presented in Paper 2.Rickert et al. presented a design for circular Bragg gratings for the telecom O–band from which the authors expect 77% coupling efficiencies into single modetelecom fibers [255]. Also approaches that directly fiber couple the quantum dotare of interest for better integration into fiber–based networks as demonstratedfor example by Musia�l et al. where a high NA fiber was precisely glued ontop of an InGaAs/GaAs O–band quantum dot and yielded detection rates of73 kHz [256]. Interestingly the authors used a compact Stirling cryocooler tocool their quantum dots, which makes the source more deployable than usualbulky experimental setups.

Chapter 5

Quantum dot tuning techniques

The stochastic nature of the growth process of self–assembled optically activesemiconductor quantum dots leads to a distribution in quantum dot size andshape, as well as composition and strain gradients within the quantum dots. Thisin turn leads to a spread in quantum dot emission energies, biexciton bindingenergies and can cause a non–zero finestructure splitting. The dissimilarityof quantum dot sources is a major issue that needs to be addressed to boosttheir applicability in quantum technologies. While growth techniques are beingdeveloped towards the yield of very similar QDs without finestructure splitting[257], it is very unlikely that they will eventually produce QDs that are thesame in every atom. Post–growth techniques to tune the emission energyto resonantly overlap remote QDs or to reduce the finestructure splitting arematuring simultaneously. Notably, strain tuning has been established as a tuningtechnique that provides repeatable results, and can be applied independently ofthe material system or sample design, making it a tuning technique with highpotential scalability. In this chapter, I will give an overview of the most commontechniques for tuning the quantum dots’ emission energy and finestructuresplitting. I will also sketch tuning techniques that have been used for quantumdots in the telecom range. Moreover, a detailed introduction to strain tuningwill be given including the physical background, a typical device design andexperimental results.

5.1. Overview of tuning techniquesTuning of quantum dot emission wavelengths has been achieved via temperaturetuning, often with the intention of tuning a quantum dot into resonance with acavity [196], [200], however is not the first choice for the generation of highlyindistinguishable photons due to phonon–induced detrimental effects [203]. Lat-eral and vertical electric fields [114], [258]–[260], magnetic fields [100], [103],[261], as well as strain tuning [117], [262]–[264] have been studied as well. It hasto be noted that by applying one of the previously mentioned tuning techniquesto a quantum dot (with the exception of biaxial strain tuning), both the emissionwavelength and the finestructure splitting will be influenced simultaneously.Another issue is the coherent coupling of the two exciton levels leading to alower bound on the achievable finestructure splitting, which has been foundboth in theory [265], [266] and in experiment [260], [264]. This bound can be

33

34 5. Quantum dot tuning techniques

circumvented by using not only one ’tuning knob’ like an external electric field,but instead a combination of independent tuning knobs. A demonstration ofthis behavior e.g. with a combination of an electric field and strain [123], allowedto experimentally generate entangled photon pairs with a concurrence of 0.75(see also Section 2.4) [121]. Alternatively three independent strain axes thatallow to control finestructure splitting and emission wavelength without mutualdependence have been realized and allowed to demonstrate an entanglementfidelity of 80% [122] while being on resonance with the D1–transition in Cesium.With a similar device and a resonant excitation technique, fidelities as high as97.8% could be observed.All of the above mentioned tuning techniques have also been employed to overlaptwo remote quantum dots and perform two–photon interference (TPI) experi-ments (for these experiments remote indicates that the quantum dots are inseparate cryostats, not necessarily referring to large spatial separation): temper-ature tuning [267]–[269], tuning with electric field [270], magnetic field [271], andstrain [149], [272], [273]. In most of the experiments, two–photon interferencevisibilities below 50% have been reached. At the time of writing this thesis, thehighest TPI visibility achieved for two remote quantum dots on–demand is byReindl et al. [149]. By using phonon–assisted two photon excitation and straintuning to overlap the biexcitons of two quantum dots the authors realized a TPIvisibility of 51%. Another approach along these lines that should be mentionedhere is to overlap two remote quantum dots via quantum frequency conversion(see also Section 3.3.2). Weber et al. demonstrated a TPI visibility of 29%after converting photons of two quantum dots with emission around 900 nm tothe telecom C–band [179]. This approach provides the largest ’tuning range’granted the availability of a suitable laser source and non–linear crystal toperform the conversion with a specific quantum dot. While quantum frequencyconversion offers great flexibility, it comes with the additional cost of requiringmore support equipment and a finite conversion efficiency (around 30% for eachconversion process in Ref. [179]).With regard to integration of multiple sources in quantum networks, implement-ing tuning knobs for wavelength and finestructure splitting is a continued effortfor quantum dots emitting in the telecom range. Integrating of InAs quantumdots in a p–i–n structure and applying electric fields allowed to simultaneouslytune both the emission wavelength and the finestructure splitting. This wasdemonstrated by Ward et al. [157] with a tuning range of ≈ 0.225 nmcmkV−1.InAs/InP quantum dots with emission in the telecom C–band have been stud-ied in magnetic fields, however in the context of measuring the electron andhole g–factors and not specifically for wavelength tuning [274]. Integration ofquantum dot samples onto piezo–electric substrates has been used to influenceboth emission wavelength and finestructure splittings of quantum dots in thetelecom range. Sapienza et al. studied the effect of uniaxial stress on thefinestuctures splitting of InAs/GaAs quantum dots emitting between 1.1μm to1.3μm. Piezo–tuning of an InAs/GaAs quantum dot in the telecom O–bandwas demonstrated by Hofer et al. [275]. The authors applied uniaxial strain

5.2. Strain tuning 35

to a quantum dot membrane, which simultaneously influenced both emissionwavelength (1.88 nmkV−1) and finestructure splitting of the quantum dots. Ourresults on biaxial piezo–tuning of telecom C–band InAs/GaAs quantum dotsare summarized in Paper 3 with a tuning range of 0.31 nmkV−1 and a stabilityof the target wavelength of (2.43± 0.07) pmh−1.

5.2. Strain tuningThe ability to being able to reversibly control quantum dot properties viastrain tuning lies in the piezoelectricity of the used substrates. Directionaldeformation of piezoelectric materials causes a polarization of the material, asthe centers of mass of positive and negative charges no longer coincide. Thisgenerates microscopic dipoles within the unit cell. Summing up the dipolefields throughout the crystal can lead to a measurable voltage. In turn, thiseffect can be reversed such that the application of a voltage to a piezoelectricmaterial leads to a deformation. This enables us to strain quantum dots byapplying a voltage to a device consisting of a quantum dot sample mountedto a piezoelectric substrate. The piezoelectric effect occurs in the materialsthat exhibit no inversion symmetry and was discovered in 1880 by Jaques andPierre Curie [276]. Typical materials in this context are Pb(Zr,Ti)O3 (PZT) orPb(Mg1/3Nb2/3)O3–PbTiO3 (PMN—PT) [277]. Within these materials areaswith dipoles oriented in the same direction are referred to as so–called Weissdomains. These domains are however usually randomly oriented, leading to asmall or negligible overall electric field. To overcome this, piezoelectric materialscan be poled by applying an external electric field. This process aligns thedomains along the field. Even after removal of the external field, the domainsstay aligned and a permanent polarization is remaining. This poling process istypically performed at room temperature and results in a poling–I–V–curve asin Figure 5.1 (a). The shape of the curve can be explained in the following way:the alignment or flipping of each domain causes a small current to flow. Withincreasing applied voltage the domains start to flip, leading to a rising currentflow. At some point most of the domains have been forced to align followingthe applied voltage, the change in current is saturating (peak at 45V) and isthen decreasing as less and less domains are left that haven’t been aligned yet.During the cooldown process the external voltage is held (typically at 100V) toavoid spontaneous depolarization of the domains.The devices in Papers 3 and 7 are based on PMN-PT piezoelectric substratesfrom the company TRS Technologies with a thickness of 200μm and 〈001〉crystal orientation. As the electric field within the piezoelectric substrate isinversely proportional to the thickness of the substrate, thinner substrates canproduce higher strain at a given voltage [277]. For this reason, the piezo–electricsubtrates used for tuning quantum dots are mechanically thinned prior tocoating the piezo with gold. The tuning range of the strained quantum dotsis dependent on the sample thickness [278]. We have used two methods toreduce the sample thickness, a mechanical lapping process described in Paper3 and a chemical back–etching process to remove the substrate (described in

36 5. Quantum dot tuning techniques

Paper 7). While chemical etching can yield thinner samples, the mechanicalprocess comes with the advantage of being applicable for any sample design(no sacrificial etch stop layer required) and even pre–existing DBRs can betransferred onto the piezoelectric substrate. To rigidly attach the sample to thepiezoelectric substrate we have used either cryogenic epoxy (Stycast 2850FT,in Paper 3) or the photoresist SU8 (in Paper 7). SU8 can be applied to thesubstrate very evenly via spin–coating and it has recently been shown that itdelivers an outstanding strain transfer [279]. A typical device design for straintuning a quantum dot sample is shown in Figure 6.5 (a).In the strain tuning experiments a high voltage source (Keithley 2410) isemployed to deliver voltages between −400V to 800V. When strain is appliedto a quantum dot, its emission energy is shifting because the interatomicdistances are changed [280]. This is shown in Figure 5.1 (b) for a quantum dotwith emission within the telecom C–band that was tuned from 300V to −300Vand then to 600V. For this sample the substrate was chemically removed,leading to a quantum dot membrane with a thickness of 2μm. An overall tuningrange of 1.57 nmkV−1 can be observed in the color–coded intensity map.

Pie

zo v

olta

ge (

V)

+300

-300

+600

1549.2 1550.5 1551.8Wavelength (nm)

min

max

Piezo voltage (V)0 50 100

Cur

rent

(μ

A)

0

3

6(a) (b)

Figure 5.1: (a) Piezo poling current as a function of applied voltage. (b)Reversible wavelength tuning of a quantum dot in an approximately 2μm thickmembrane.

Chapter 6

Devices studied in this thesis

In this chapter, I discuss the different types of semiconductor quantum dotsthat were used during the course of this thesis and in the articles in Part II. Ingeneral, three types of quantum dots have been studied, namely InAs/GaAsquantum dots with emission in the telecom C–band, InAsP quantum dots inInP nanowires whose emission was shifted from 900 nm to 1500 nm to achievephotons in the telecom range and GaAs/AlAs quantum dots with emission closeto the Rubidium D1 transition at 795 nm. I focus mostly on the growth methodsand used material systems, as well as relevant previous results obtained withthe type of quantum dots, if applicable. Furthermore, typical quantum dotproperties, such as emission wavelength, finestructure splitting and biexcitonbinding energies will be mentioned.

6.1. InAs quantum dots at telecom wavelengthsThe InAs/GaAs quantum dots with emission around 1.55μm were grown byour collaborators in Prof. Mattias Hammars group at the school of electricalengineering and computer science at KTH. The recipe for low–density singlephoton emitting quantum dots on GaAs substrates with a so–called metamorphicbuffer layer was developed in the group of Prof. Peter Michler at the Universityof Stuttgart [139]. As discussed in more detail in Section 3.3.2, the metamorphicbuffer provides an almost lattice matched interface between the GaAs substrateand the InAs quantum dots, enabling emission in the telecom C–band. Thesamples are grown by metal–organic vapor–phase epitaxy. Below the quantumdot layer, a distributed Bragg reflector is grown consisting of 20 pairs ofAlAs/GaAs layers with nominal thicknesses of 82 nm and 130 nm, respectively.The metamorphic buffer layer begins with In0Ga1As (pure GaAs), the Indiumcontent is increased quadratically to In0.4Ga0.6As at the top of the nominally1150 nm thick layer. Both the DBR and the MMBL are grown at 670 °C,whereas the quantum dot growth is taking place at 545 °C. The quantum dotgrowth temperature has been optimized for minimized finestructure splitting.The quantum dots are capped with an In0.35Ga0.65As layer of nominally 250 nmthickness. From this type of quantum dots, single photon emission with g(2)(0) =0.184 under pulsed above–band excitation has been obtained [139], as well aspolarization entangled photon pairs with a fidelity of 61% [172]. The epitaxialgrowth mode via an industry–grade growth technique in combination with the

37

38 6. Devices studied in this thesis

1540.0 1545.0 1550.0

0.805 0.803 0.801

0

1

2

3

Inte

nsit

y (k

cts.

/s)

Wavelength (nm)

X

XX

Energy (eV)(a) (b)

3 μm

Figure 6.1: (a) Cross–sectional scanning electron microscope (SEM) image ofthe sample used in Paper 8. The DBR mirror is visible in the lower half of theimage with high contrast between AlAs (black) and GaAs (gray) layers. On topof the DBR, the metamorphic buffer layer, quantum dot layer and capping layerare visible, however hard to distinguish due to low composition gradient. SEMimage courtesy of Stephan Steinhauer. (b) Typical spectrum from a quantumdot from the sample used in Paper 8 under above–band excitation. Exciton andbiexciton state are marked in the graph.

GaAs material platform that enables growth of high index contrast DBR mirrorsmakes these quantum dots viable candidates for scalable sources of quantumstates of light in the telecom C–band. In experiment, we have observed typicalbiexciton binding energies of 2meV to 2.5meV, average linewidths below 50μeVand a mean finestructure splitting of 9μeV. The InAs/GaAs quantum dots havebeen transferred to a piezo–electric substrate and subsequently strain–tuned,which is discussed in Paper 3. In Paper 5 a commercial phase modulatorhas been used to generate single photon sidebands and study the resultingsingle photon purity. Moreover, resonant excitation schemes for addressingthe biexciton–exciton cascade have been investigated in Paper 8 for generatingsingle and entangled photons on demand.

6.1.1. Planar cavity designFor the InAs/GaAs quantum dots, a planar cavity has been employed in orderto enhance the extraction efficiency. For the telecom InAs/GaAs QDs, theplanar cavity is formed between 20 Bragg mirror pairs below the QDs andthe semiconductor–air interface at the top of the sample. Here, the QDs are

6.1. InAs quantum dots at telecom wavelengths 39

Distance from surface (μm)0 1 2 3 4 5 6

0

1

2

3

4F

ield

int

ensi

ty (

a.u.

)

Ref

ract

ive

inde

x (a

.u.)

0

1

2

3

4(a)

1300 1400 1500 1600Wavelength (nm)

0.0

0.2

0.4

0.6

0.8

1.0

Ref

lect

ivit

y (a

.u.)

(b)

Field intensityRefractive index

MeasuredSimulated

Figure 6.2: (a) Refractive index as a function of distance from the sample surfacefor sample 8344 (light blue). The layer thicknesses were extracted from SEMmeasurements performed by Stephan Steinhauer. The simulated field intensity(dark blue) for the measured layer thicknesses obtained via the transfer matrixmethod. (b) DBR reflectivity obtained from simulation (pink) and measurement(dark blue).

embedded in a 3λ–cavity due to thickness of the MMBL which is typically at least1μm to avoid cracking. In contrast to other planar cavities, like the micropillarcavities discussed in 4.1, the mode volume is much larger as the structure isnot exhibiting boundaries in the vertical direction. For the telecom QDs, therequired layer thicknesses have been investigated via the so–called transfermatrix method (TMM) with a program provided by Dr. Thomas Schwarzbeckfrom the University of Stuttgart. The TMM uses multi–beam interference tocalculate the resulting electromagnetic field in a stratified medium. This can beused to design DBR mirrors, sample structures and anti–reflection coatings formaterials with known refractive indices. In Figures 6.2 and 6.3 results from suchcalculations are shown for an existing sample and an ideal (simulated) sample,respectively. For the existing sample 8344 shown in Figure 6.2 we noticed inphotoluminescence measurements that the emission of the QDs was not as brightas expected. A detailed discussion of the used setup and measurement techniqueis given in Chapter 7. With the thicknesses obtained via SEM by StephanSteinhauer and the compositions/refractive indices measured via secondary–ionmass spectroscopy (SIMS) measurements by the company Probion Analysis, wecould use TMM to understand the underlying issue. The field intensity exhibitsa minimum at the quantum dot position shown in Figure 6.2 (a), leading toan inhibited excitation and subsequent emission of the quantum dots. It canalso be seen that the field intensity decays slowly within the DBR but still


Figure 6.3: (a) Refractive index (light blue) and field intensity (dark blue) as afunction of distance from the sample surface for an ideal sample with optimizedthicknesses for maximum field intensity at the quantum dot position. (b) DBRreflectivity obtained from simulation (pink) with the transfer matrix methodwith layer thicknesses for maximum reflectivity at 1550 nm.

shows slightly higher intensities deeper within the structure. This can alsobe understood with the reflectivity data presented in Figure 6.2 (b). Here,the spectral region with maximum reflectivity, the so–called stopband is notcentered around 1550 nm, but in the vicinity of a local minimum at this position.To demonstrate the accuracy of the method, the simulated data is underlaidwith measured reflectivity data reveiling very good agreement. In comparison,in Figure 6.3 the field intensity, refractive indices and reflectivity for an idealsample with optimized thicknesses for maximum extraction efficiency are shown.Here, there is a maximum of the field intensity at the quantum dot positionand the field is decaying quickly within the DBR.

6.2. InP dots in nanowires emitting at telecom wavelengthsThe InAsP/InP nanowire quantum dots studied during this thesis were grownby our collaborators at the National Research Council in Ottawa, Canada in thegroup of Dan Dalacu and Philip J. Poole. These nanowires emit in the rangebetween 880 nm to 1550 nm and the growth has been performed with emphasison optimizing the growth process and structure dimensions for emission attelecom wavelengths. The growth process is a combination of selective–areagrowth with vapor–liquid solid growth. To enable selective–area growth, theInP substrate is covered by a dielectric mask (Silicon Dioxide) with circularopenings that are defined via electron beam lithography. The openings contain acircular gold droplet acting as a catalyst for the vapor–liquid–solid epitaxy. The

6.2. InP dots in nanowires emitting at telecom wavelengths 41

quantum dot contained in the nanowire is grown by switching the precursorsfrom the host material to the quantum dot material [226], [227]. The waveguideis grown by cladding the nanowire, the final diameter is imposed by the diameterof the opening to the substrate in the mask. A taper has been added to reduceback–reflections and divergence of the photons leaving the top of the waveguidewhich facilitates efficient coupling to external optics [223]. Nanowire quantumdots have been predicted to exhibit a vanishing finestructure splitting basedon their symmetry [105] and experimentally low splittings have been foundon the order of (3.4± 3.0) μeV [234]. The emission of polarization entangledphoton pairs with fidelities >75% have been experimentally verified [234]–[237]. Furthermore, the photons emitted from the nanowire waveguide are in aGaussian mode which is ideal for coupling the emitters to optical fibers [238].The multiphoton emission probability has been measured to be below 1%.The InAsP/InP nanowire quantum dots have been investigated in Paper 2 inview of how the emission of the quantum dots can be shifted from around900 nm to telecom wavelengths and how this affects decay times and singlephoton emission. For the sample studied in Paper 2, we observe an average

1311.0 1312.5 1314.0

0.946 0.945 0.944

0

5

10

15

20

Inte

nsit

y (k

cts.

/s)

Wavelength (nm)

Energy (eV)

X

XX

(a) (b)

Figure 6.4: (a) Microscope image of the nanowire quantum dot sample used inPaper 2. The sample is structured into square shaped areas via electron beamlithography that contain the studied nanowires in their center. The e–beamdose determining the nanowire diameter is marked for each square. (b). Typicalspectrum from a nanowire quantum dot, here with emission within the telecomO–band. Biexciton and exciton emission lines are markes in the spectrum.


finestructure splitting of 6μeV, linewidths of 100μeV and biexciton bindingenergies of around 3meV to 4meV.

6.3. GaAs quantum dots at Rb wavelengthThe GaAs quantum dots studied in this thesis are grown by our collaboratorsat the Johannes Kepler University in Linz by the group of Armando Rastelli.The emission wavelengths of these quantum dots are in the range of 780 nm to800 nm, in the vicinity of the D1 transition in Rubidium, making them suitablefor coupling to the atomic transition for single photon storage [281]. Thequantum dots are grown by molecular beam epitaxy via the so–called dropletetching method. During the growth, an Al0.4Ga0.6As layer is deposited ontoa GaAs substrate as a host material for the quantum dots. This is followedby a deposition of metallic droplets (Ga) which generates holes based on localdroplet etching [106], [282]. This hinges on an Al gradient between the surfaceof the AlGaAs layer and the Ga droplet. The holes are consecutively filledwith GaAs as a low bandgap semiconductor material to generate the quantumdots. The quantum dots are placed within a λ–cavity with 9 pairs of AlGaAs(Al0.95Ga0.05As and Al0.2Ga0.8As) distributed Bragg reflectors (DBR) belowand 2 pairs on top for enhanced extraction efficiency (see also Chapter 4). Thisgenerates highly symmetric quantum dots, with average finestructure splittingsas low as (3.9± 1.8) μeV [108]. Entangled photons generated by these quantumdots have been observed [99], [283] with near–unity fidelities. Based on thealmost lattice matched GaAs/AlGaAs interface the quantum dots are strainfree compared to self–assembled Stransky–Krastanov quantum dots.Droplet etched GaAs quantum dots have been used to demonstrate singlephoton emission with record low background emission in Paper 1, to generateindistinguishable photons via resonance fluoresence without the need for cavityenhancement in Paper 4 and to demonstrate entanglement swapping in Paper6. They have been embedded into micro–parabolic resonators to generate abroadband tunable microstructure for enhanced extraction efficiency in Paper7. Their behavior concerning resonant s–shell excitation versus two–photonresonant excitation has been studied to investigate limitations of single photonpurity and indistinguishability based on the excitation method in Paper 9. TheGaAs quantum dots exhibit typical linewidths of 20μeV, finestructure splittingsof 5μeV and biexciton binding energies of 3meV to 3.5meV.

6.3.1. Micro ParabolasA broadband microcavity design based on the concept of a parabolic mirror hasbeen designed, and has been subsequently fabricated by Thomas Lettner. Thekey considerations in the development process were to create a microstructurewith broadband enhancement, an emission profile that is optimized for fibercoupling and also integrable with piezoelectric substrates. The broadbandenhancement should allow to enhance not only a specific quantum dot transitionon resonance with the cavity but instead work at least for both transitions

6.3. GaAs quantum dots at Rb wavelength 43

790.0 792.5 795.0 797.5 800.0

1.570 1.565 1.560 1.555 1.550

0

5

10

15

Inte

nsit

y (k

cts.

/s)

Wavelength (nm)

Energy (eV)(b)(a)

X X*

Figure 6.5: (a) Image of a typical sample design for the GaAs quantum dots.The mechanically thinned sample (dark gray) is glued to a piezoelectric substrate(gold) for emission energy tuning. A solid immersion lens is added for enhancedextraction efficiency. Sample preparation by Thomas Lettner. (b) Typicalspectrum from a quantum dot from the sample used in Papers 1, 4, 9. Excitonand charged exciton state are marked in the graph.

for the radiative cascade. More preferably the structure should provide anenhancement for the majority of quantum dots within the ensemble consideringthe stochastic growth process of self–assembled QDs. A near–Gaussian emissionprofile would be ideal for efficiently coupling to optical fibers. Strain–tuningthe QD in the cavity allows to modify the emission wavelength [280], [284]–[286]. The concept of the device is to place the quantum dot at the focal pointof the parabolic mirror, such that the emission into 4π is redirected towardsthe collecting optics. In Figure 6.6 (a), a sketch of a parabolic micro cavitycontaining a quantum dot is shown. In finite–difference time domain (FDTD)simulations the properties of such a structure have been studied, in particularthe device dimensions, the emitter position and the farfield emission profile.The results of the simulations are presented in Paper 7 alongside with thefabrication methods and experimental results. The fabrication method hasbeen developed by Thomas Lettner and consists of the following steps: Theposition and diameter of the paraboloid are designated by optical lithography.After exposure the resist is reflown [287] to achieve a parabolic shape that istransferred into the sample via reactive ion etching. The structures are thengold–coated and can be integrated onto piezo–electric substrates after backetching. In Figure 6.6 (b), the spectrum of a quantum dot in a parabola is


compared to the on of a quantum dot on the as–grown sample. On average,an order of magnitude of increase in brightness is gained when the quantumdots are integrated into parabolic microcavities. It has to be noted that thestructures presented in Paper 7 are produced from periodic arrays of etchingmasks. Deterministic integration would boost the yield and performance. Thefabrication process has been developed and demonstrated for GaAs/AlGaAsquantum dots, but could potentially be transferred to other material systems.

f

d

(a)

air

AlGaAs

(b)

780 790 800Wavelength (nm)

0

5

10

15

Inte

nsit

y (a

. u.)

as-grownParabola

QD

x10

Figure 6.6: (a) Schematic description of a micro parabolic mirror. (b) Spectraof quantum dots of the unprocessed sample (dark blue) and in a micro parabola(pink).

Chapter 7

Cryogenic micro–photoluminescence

Confocal micro–photoluminescence measurements at cryogenic temperaturesare performed in order to purposely address single quantum dots. Cooling thesample to cryogenic temperatures (typically 4K to 10K) allows to isolate thequantum system from the environment since the confinement energies are muchsmaller compared to thermal energies at room temperature (≈ 25meV). Inthe subsequent chapter I will discuss the working principle behind a micro–photoluminescence setup and discuss the required components, also in view ofrequirements for being able to perform measurements at telecom wavelengths.Moreover, I will discuss experimental techniques ranging from basic samplecharacterization to more sophisticated resonant excitation techniques.

7.1. SetupThe micro–photoluminescence setups used for the experiments presented in partII are consisting of three main parts: an excitation laser, a cryostat containingthe sample including a microscope objective or lens to excite the quantum dotand collect the emission, and finally a spectroscopy and detection setup thatcan also include more intricate filtering components. A schematic illustrationof a typically used modular micro–photoluminescence setup is presented inFigure 7.1. As previously discussed in Chapter 3.3, all quantum dots studiedin this work are excited optically with either of the laser sources presented intable 7.1. Depending on the specific requirements of a given experiment, e.g.excitation wavelength or continuous wave (cw) vs. pulsed excitation, a suitableexcitation laser is chosen and can be coupled into the setup by using opticalfibers for the corresponding laser wavelength. An overview of the differentlasers and their properties is given in Table 7.1. A schematic of a pulsedlaser used for most experiments in II is shown in Figure 7.1 (a). After thelaser, a pulse slicer with adjustable slit width consisting of reflection gratingssets the spectral bandwidth of the laser pulses. After the pulse slicer, thelaser is fiber coupled and can be brought to the cryostat (Figure 7.1 (b)). Areflective collimator is used to collimate the excitation laser independently ofits wavelength. This is followed by a polarizer, halfwave plate and anotherpolarizer, which allows to control the laser power exciting the quantum dot.A non-polarizing beamsplitter with 90:10 (T:R) splitting ratio combines theexcitation laser sent into the cryostat in reflection and the quantum dot photons

45

46 7. Cryogenic micro–photoluminescence

NA=0.8

Figure 7.1: Schematic of our modular micro-photoluminescence setup. (a)Pulsed excitation laser with pulse slicer to control the pulse bandwidth. (b) Thequantum dot setup. The excitation laser is power controlled with a combinationof a polarizer, a motorized half waveplate and another polarizer. The excitationlaser is then coupled into the cryostat with a 90/10 beamsplitter and focusedwith an objective inside the cryostat onto the sample. The quantum dot photonsare fiber coupled and can be brought either to a commercial spectrometer (c)for spectral analysis or narrow band filtering that can for example be performedwith a transmission spectrometer (d).

7.1. Setup 47

Laser Wavelength(nm)

Type Linewidth (kHz)

HeNe 632.8 cw 2.5 · 105TopticaDLPro 765-805 cw 50

TopticaCTL1550 1520-1630 cw 10Laser Wavelength

(nm)Rep. rate (MHz) Pulse length

APEPicoEmerald 1 650-990 and1080-2490

80 2 nm to 0.02 nmor 2 ps to 100 ps

APEPicoEmerald 2 700-900 and1080-1950

320 2 nm to 0.02 nmor 2 ps to 100 ps

Table 7.1: Continuous–wave (cw, top part) and pulsed lasers (bottom part)used for the experiments discussed in this thesis.

that pass the beamsplitter in transmission. The beamsplitter is coated forthe range of 1050 nm to 1700 nm to optimize the collection of the quantumdot photons. The quantum samples are mounted in a closed–cycle cryostatwith optical access (Montana instruments, Cryostation s50) on top of a stackof nano–positioners (Attocube 2x ANPx101 and ANPz101). Experiments aretypically performed at 8K. Inside the cryostat a microscope objective (OlympusLCPLN100XIR, working distance 1.48mm) is used. This so–called confocalmicroscope focuses the excitation laser onto the sample with a spot size of≈ 2μm and also collecting quantum dot emission from the same spot. With thegiven spot size single quantum dots can be individually addressed given suitablylow quantum dot density on the sample (on the order of 107 QDs cm−2). Inthe following, the emitted quantum dot photons are coupled into a single modeoptical fiber (SMF–28) using a lens based fiber–collimator with a beam diameterthat is matched to the aperture of the microscope objective (Schafter Kirchhoff,60FC). This optical fiber can now be connected e. g. to a spectrometer(Acton SP2750i) with 750mm focal length and an 830mm−1 grating (sketch inFig. 7.1 (c)). The commercial spectrometer is equipped with an InGaAs array(Princeton Instruments OMA V) with 1 x 1024 pixels for spectroscopy in therange of 1000 nm to 1600 nm. The typical pixel–to–pixel resolution is 0.05 nmor 25μeV for a slitwidth of 25μm and a wavelength of 1550 nm. In front ofthe spectrometer a motorized half waveplate and a polarizing beamsplitter canbe placed to perform polarization resolved measurements (see Section 7.2.2).Alternatively the optical fiber carrying the quantum dot photons can alsobe connected to a home–built transmission spectrometer (Fig. 7.1 (d)) fornarrowband optical filtering (0.15 nm full width half maximum) and an end–to–end efficiency of ≈ 60% for each of the two outputs. Detailed informationon the setup of the transmission spectrometer, the used components and the


achieved specifications are given in Chapter A. The filtered output of thetransmission spectrometer can be connected to superconducting single photondetectors (SSPDs) with a temporal resolution of 15 ps, 30 s−1 dark countsand an efficiency of 15% and 25%. With the SSPDs, measurements basedon photon counting can be performed, e.g. lifetime measurements, auto– orcross–correlation experiments (see Chapter 8).

7.2. Characterization measurementsIn the following I will discuss two types of measurements that gave us a lotof insight into the properties of the quantum dot samples and proved to beespecially helpful for the InAs/GaAs quantum dots that were developed inclose collaboration with the growers at KTH (group of Prof. Mattias Hammar).Key characteristics that I was looking for was emission in the telecom C–band,suitable quantum dot density and a homogeneous quantum dot distribution.Additional properties that were monitored were the finestructure splitting ofthe quantum dots and the emission intensity.

7.2.1. MappingAcquiring photoluminescence maps (PL–map) of samples has proven to be auseful tool to efficiently get insight into many key properties of a sample underinvestigation. For the measurement of a PL–map the same setup as in theprevious section is used. The quantum dots are excited above–band (see alsoSection 7.3) with an excitation power close to saturation. Within a predefinedarea, e.g. 50μm× 50μm spectra are taken in regular steps, for example every0.5μm. This is done by moving the excitation/detection spot across the sampleby moving it with the nano–positioners by the specified amount usually in ameander shape. To gain a first understanding of the investigated sample, weplot the maximum intensity found in each spectrum over the spatial coordinate.From this, we can directly draw conclusions about the number of optically activequantum dots in the scanned area, thus, the quantum dot density. To gainmore knowledge, we can fit each spectrum and extract the center wavelengthand peak area for each emitting quantum dot. In order to optimize the fittingbehavior, a threshold for the minimum peak height to be fitted is set.I used this technique especially to give feedback to the growers at KTH de-veloping the InAs/GaAs quantum dots. Usually in the early stages of sampledevelopment, one would perform macro–photoluminescence experiments in orderto quickly collect data on the quantum dot ensemble from a sample grown withnew parameters. As we did not have a macro–PL setup in the beginning of theproject, I used PL–mapping as a substitution. Moreover, PL–mapping can alsobe a useful tool to visualize emission from patterned samples or microstructures,since the regularly spaced emission will also show up in the PL–map. Theresolution of the PL–maps is mostly limited by the readout accuracy of the piezoactuators, which is approximately 500 nm. In Figure 7.2 (a) a PL–map of asample with emission in a range of 1535 nm to 1565 nm is shown with a density

7.2. Characterization measurements 49

of optically active quantum dots of approximately 5 · 106 QDs cm−2. To obtainthe map, all spectra with peak intensities larger than 200 counts/s where fittedand the peak area is plotted over the x– and y–position. Due to inaccuraciesin the piezo positioner readout, the map looks slightly warped at the edges.This is something that should be accounted for to obtain spatially very reliablemaps of samples, but can be neglected when using mapping to gain statisticsof samples. A histogram of emission wavelengths is presented in Figure 7.2(b). The quantum dot emission of the investigated sample is spread within thetelecom C–band with a slight trend towards longer wavelengths above 1555 nm

0 10 20 30 40

0

10

20

30

40

50

y -

posi

tion

(m

)

x - position ( m)

Area

1535

1540

1545

1550

1555

1560

1565

0 50 100 150

Wav

elen

gth

(nm

)

Count

min

max

(a) (b)

Figure 7.2: (a) PL–map of the sample 7896 within a range of 50×50μm2. Thecolor–coded map depicts fitted peak intensity within the range between 1535 nmto 1565 nm. (b) Histogram of fitted center wavelengths of within the scannedarea.

7.2.2. Polarization–dependent measurementsAnother property of the quantum dots that is of great interest is the finestructuresplitting (FSS) of the exciton state. The origin of the FSS is discussed in Section3.3.1 and its importance in sight of the emission of entangled photons by quantumdots in 2.4. The finestructure splitting in quantum dots investigated in thisthesis is in most cases smaller than the spectrometer resolution and can thus notbe directly observed in a non–polarization resolved single PL spectrum. However,it is possible to selectively suppress either of the polarization components andthen fit the resulting spectrum to surpass the spectrometer resolution. In orderto experimentally determine the FSS of a quantum dot a motorized waveplate


and a polarizing beamsplitter are placed in front of the spectrometer (see Figure7.1 (b) in brackets). The waveplate is then moved in steps of 1°, while aspectrum is recorded for each step. With the rotation of the waveplate, thepolarization component in the biexction or exciton emission that is transmittedthrough the polarizing beamsplitter is gradually changed. This is continuouslysuppressing the horizontal (vertical) component depending on the start positionof the waveplate. By fitting the spectra and extracting the center wavelength,the resulting polarization dependent center wavelength of the biexction andexciton can be obtained and this wavelength will be oscillating slightly due tothe presence of the FSS [113]. This behaviour is schematically visualized inFig. 7.3(a)–(d). Biexciton and exciton center wavelengths are oscillating witha π phase shift because a red shift of the exciton emission due to polarizationsuppression is causing a blue shift of the biexciton emission and vice versa (Fig.7.3(e)). This means in turn that finding two counter–oscillating emission linesfrom a quantum dot with the same amplitude, it is likely that a biexciton–excitoncascade has been identified (proof can however only be obtained by measuringcross–correlation between the two emission lines in question). Systematic errors,e.g. drifts influencing both biexciton and exciton emission can be removedby subtracting the fitted energies from each other for each wavelength angle.This method allows to determine a quantum dot’s finestructure splitting withresolutions below 1μeV [113], [260].

HVsum

CCD intensity

CCD intensity

Fitted intensity

Fitted intensity

I

E

I

E

I

E

I

E

(a) (b)

(c) (d)

Ene

rgy

(eV

)

Waveplate angle ( )

(e)

XXX

Figure 7.3: (a) Measured CCD intensity separated into horizontal (light bluedashed line), vertical (dark blue solid line) polarization components and observedsum of both components (black dashed–dotted line) for a HWP angle of α. (b)Actual intensity obtained via a fit to the data (black line) and the horizontaland vertical components for a HWP angle of α. (c) Measured intensity fora HWP angle of α + 90◦. (d) Fitted intensity for α + 90◦, note the shiftedenvelope function. (e) Fitted biexciton and exciton energies for a full rotationof the used half waveplate. The finestructure splitting corresponds to 6μeV.

7.3. Excitation techniques 51

7.3. Excitation techniquesSo far, I have only talked about optical excitation in a very general manner,i.e. to generate charge carriers that will populate the quantum dots states.However, the excitation technique has a pivotal effect on the properties ofthe generated photons especially depending on whether it is a resonant ornon–resonant excitation process. Before going into any more detail concerningthe excitation wavelength and the resulting emission properties, we can alreadymake a first division between continuous wave and pulsed excitation. In thecase of cw excitation, charge carriers are created continuously, enabling animmediate re–population of the quantum dot as soon as it has decayed. Thisis typically leading to higher observed count rates, yet does not allow us todraw any conclusion on the temporal emission properties of the quantum dotphotons. In pulsed excitation techniques, the excitation of the quantum dotcan always be related in time to the sync of the excitation laser. This allowsfor example to determine the decay time of a specific quantum dot state, whichis discussed in more detail in Chapter 2. Some of the pulsed excitation schemesenable on–demand generation of single and/or entangled photons.

7.3.1. Above–band excitationAbove–band excitation is a non–resonant excitation technique that includesessentially all wavelengths with energies larger than the bandgap energy thatdo not address a specific resonance like the s–, p– or d–shell. Due to theexperimental simplicity of using above–band excitation, it is often used forsample characterization, as the requirements on the laser wavelength andbandwidth are low (no specific resonance has to be addressed). Moreover,filtering the laser from the quantum dot emission is simple as they are spectrallywell separated. For the InAs/GaAs quantum dots characterization measurementswhere performed using a cw HeNe laser or the signal of the PicoEmerald atwavelengths of around 780 nm. The relaxation of the charges generated viaabove–band excitation is fast for InAs quantum dots (on the order of a few10 ps [288]) and not negligible for GaAs quantum dots (on the order of 900 ps inReference [289]). In either case this causes a non–negligible time–jitter in termsof photon emission time relative to the excitation laser, making this excitationmethod unsuitable for the generation of highly indistinguishable photons [288],[290]. Interactions between relaxing charge carriers and impurities or trapscan homogeneously broaden the transitions [291] and cause decoherence of theemitted photons.

7.3.2. S–shell resonant excitationResonantly addressing the neutral (X) or charged exciton (X*) yields theemission of resonance fluorescence (RF) photons (the corresponding level schemeis presented in Figure 7.4 (a)). This has been experimentally demonstrated forthe first time in quantum dots by Muller et al. [292] and has since then beenemployed successfully for the generation of highly indistinguishable photons


Figure 7.4: (a) Level scheme of the RF excitation process. (b) QD Spectrumof the exciton under resonant s–shell excitation. (c) Sketch of a setup used forRF. Two polarizers are used to suppress the excitation laser, which acquires api–phase shift while passing the quarter waveplate on the way in and out of thecryostat. (d) Rabi oscillations observed under resonance fluorescence, up to 5πin excitation pulse area are visible.

on–demand e.g. for the first time by He et al. [293] for a quantum dot in amicropillar cavity. Since in this excitation technique the two–level system isdirectly controlled, the laser wavelength has to be tuned to the quantum dottransition under investigation, which allows filtering only in terms of polarization,not in terms of wavelength anymore. Such a so–called polarization suppressionsetup was first explained by Kuhlmann et al. for quantum dot excitation ina micro–PL setup [294]. Polarization suppression setups consisting of twoconsecutive polarizing elements like two polarizing beam splitters or a polarizingbeam splitter followed by a polarizer can achieve suppression of up to 8 ordersof magnitude. We used a similar setup for the measurements presented in


Papers 4 and 9. A schematic of such a setup is shown in Fig. 7.4 (c), witha corresponding spectrum in Fig. 7.4. Coherent control of the quantum dottwo–level system experimentally manifests in Rabi oscillations [292], [295]. Rabioscillations can be observed when an (artificial) atom is interacting with a lightfield that is at resonance (or close to) with the system. Rabi oscillations of aquantum dot under resonant s–shell excitation are shown in Figure 7.4 (d). Inthat case the atom can be regarded as a two–level system, as all other levelswill only interact weakly with the driving field [296]. The two remaining levelsare the ground state |0〉, with energy E0 and the excited state |1〉 with energyE1. The laser at resonance with the system causes it to be in the superpositionstate |Ψ〉 = c0 |0〉 + c1 |1〉, with the two coefficients c0 and c1 describing thewave function amplitude of the states |0〉 and |1〉, with |c0|2 + |c1|2 = 1. Thetemporal behavior of the wave function amplitudes can be obtained by solvingthe time dependent Schrodinger equation and yields |c20| = cos2

(ΩRt2

)and

|c21| = sin2(ωRt2

). This means that the probability to find the system in either

the ground or the excited state is oscillating in time with ΩR = |μ01ε0�

|, theso–called Rabi frequency. Here, μ01 corresponds to the dipole matrix elementfor the states |0〉 and |1〉 and ε0 is the amplitude of the electric field componentof the driving resonant field. This is describing a system without damping. Atheoretical description of the system with damping can be found in [53]. Thedamping is caused by decoherence, which is characterized by the decoherencetime T2 and the following relation:

1

T2=

1

2T1+

1

T∗2

(7.1)

Here, T1 is accounting for the longitudinal decoherence processes, caused e.g. byspontaneous emission. The so–called pure dephasing T∗

2 accounts for processesin which the population is not changed (also called transverse decoherenceprocesses), meaning energy conserving or near–elastic collisions that lead toa change in the phase of the wave function. Such processes are caused byinteraction with phonons [296], [297].

7.3.3. Two–photon resonant excitationFor deterministic excitation of the radiative cascade of the quantum dot, two–photon resonant excitation (TPE) can be used. In a two photon absorptionprocess the biexctiton level is coherently controlled. Experimentally, the exci-tation is tuned in between excition and biexciton emission wavelength, thenthe energy of two laser photons corresponds to the biexciton energy and areabsorbed via a virtual level. The level scheme is sketched in Figure 7.5 (a).The laser wavelength being off–resonant with both transitions of the cascadeis experimentally advantageous, as the spectral filtering is easier to implementcompared to direct resonant excitation. The excitation laser can e.g. be re-moved by reflecting it on a narrow–band notch filter. A typical spectrum of anInAs/GaAs quantum dot under TPE is shown in Figure 7.5 (b), with a sketchof the setup used in Figure 7.5 (c). Due to the coherent control of the cascade


Figure 7.5: (a) Level scheme of the two–photon excitation process. (b) QDSpectrum under TPE. Exciton (X, blue) and biexciton (XX, magenta) arespectrally well separated from the remaining laser (green). Inset: schematicspectrum. (c) Sketch of a setup used for TPE. Three notch filters are addedbefore the fiber coupling to filter out the excitation laser. (d) Rabi oscillationsobserved via TPE, up to 7π in excitation pulse area are visible.

Rabi oscillations are also observed for this excitation method. Rabi oscillationsup to 7π of an InAs/GaAs quantum dot emitting in the telecom C–band arepresented in Figure 7.5 (d). The technique has been demonstrated first byBrunner et al. [298] for excitation of the biexciton in quantum dots in 1994and later to demonstrate coherent control of the biexciton state by Stufler etal. [299] in 2006. Since then it has been employed to generate time–bin entangledphotons [300], entangled and indistinguishable photons on–demand [301] fromsingle quantum dots in planar samples and quantum dots in microstructures,such as circular Bragg gratings [219], [220]. Furthermore it has been used togenerate background–free single photons, see Paper 1 and Reference [302], andgenerate entangled photon pairs with near–unity fidelity and concurrence [283].


Photons created by this excitation technique have also been used to implementmore complex quantum optics experiments like quantum teleportation [150]and entanglement swapping, see Paper 6 and Reference [151]. As this excitationmethod deterministically prepares the radiative cascade, it is the method ofchoice for the generation of entangled photons, however the Hong–Ou–Mandelvisibility of both the generated photons is limited, which lies in the nature ofthe cascaded emission. As the exciton state has a finite lifetime, the biexcitonphotons emitted from the biexciton–exciton transition exhibit spectral broaden-ing, since the exciton level is not infinitely sharp. This in turn also leads to aspectral broadening for the emitted exciton photons, which are decaying from astate subject to timing jitter of the initial biexciton transition. The theory ofthis phenomenon and ways to overcome this by selective lifetime engineeringare presented in Paper 9. A more detailed explanation of the visibility obtainedvia a Hong–Ou–Mandel experiment is discussed in section 8.2This technique has also been used in Paper 1 to demonstrate background–freesingle photon emission. The excitation method is shielding the biexcition statefrom re–excitation and is, thus, removing a typical source of multi–photonemission from quantum dots. Due to the coherent control of the cascade, thescheme is ideal to generate entangled photon pairs [104], [237], this is alsodiscussed in more detail in 2.4. We have used TPE in Papers 1, 6, 7, 8 and 9.

7.3.4. Phonon–assisted two–photon resonant excitationWhile two–photon resonant excitation is yielding excellent results in terms ofsingle–photon purity and degree of entanglement, it has some drawbacks thatmight not make it feasible for large scale applications e.g. excitation of severaldeployed emitters within a quantum network. The disadvantages stem fromthe sensitivity of the π–pulse, which needs to be maintained to obtain optimalinversion of the three–level system along with optimal single photon purity.This is in practice very much dependent on the excitation laser having the idealwavelength and bandwidth to strike the resonance, all while the laser powerhas to be very stable. An excitation scheme that yields on par results withTPE while being more robust to fluctuations in laser power and wavelengthsis phonon–assisted resonant excitation. In this excitation scheme, the laseris detuned towards the exciton, thus, the energy of two absorbed photons isslightly higher than that of the biexciton level and is aiming at the phonon–bath.The scheme has been proposed first by Glassl et al. [303]. The state populationof the biexciton has been shown to reach near–unity values [304]–[306] usingthis excitation scheme. The relaxation from the phonon–continuum is fast,meaning the introduced additional time jitter is negligible. No additionaldrawbacks for the generation of indistinguishable photons are caused comparedto pure TPE and the scheme has also enabled the generation of indistinguishablephotons from two remote emitters [149]. Phonon–assisted resonant excitationhas been employed in Paper 8 to generate on–demand entangled photon pairsin the telecom C–band. The level scheme, a schematic spectrum and a power


Figure 7.6: (a) Level scheme of the phonon–assisted two–photon excitationprocess. (b) Schematic QD spectrum under phonon–assisted resonant excitation.(c) Integrated peak area as a function of excitation power for an exciton stateof an InAs/GaAs quantum dot emitting in the telecom C–band under phonon–assisted TPE. Note the saturating behavior for high excitation powers that isdemonstrating the robustness of the excitation scheme.

dependence of a quantum dot in tht telecom C–band under phonon–assistedtwo–photon excitation are presented in Figure 7.6.

Chapter 8

Correlation spectroscopy measurements

In the coming chapter experimental methods concerning correlation spec-troscopy are discussed. In Chapter 2, the theoretical concepts required forauto–correlation measurements (Hanbury Brown and Twiss), Indistinguishabil-ity measurements (Hong–Ou–Mandel) and entanglement measurements havebeen taken up. Now, after having discussed the properties of the quantumemitters used in this thesis and their excitation, it is time to have a look atthe experimental realization of correlation experiments at the single photonlevel. All of these measurements have in common that they require highlysensitive click–detectors that can precisely register the arrival of single photons.For all experiments, except in Paper 6, we have used superconducting singlephoton detectors (SSPDs), either optimized for 900 nm or 1300 nm. SSPDs haveemerged as high performance detectors of single photons with low timing jitter(values slightly below 10 ps can be reached today [307]) and high efficiencies(beyond 90% is now state–of–the–art [308], [309]). The detectors are connectedto a time–to–digital converter (PicoQuant Hydraharp 400, QuTools Qutag orSwabian Instruments time tagger) to record the photon detection events. If thequantum dot is excited with a pulsed laser, the laser trigger is also recorded.

8.1. Auto–correlation measurementsTo study the type of light, intensity fluctuations of the source are studied, aspreviously discussed in Chapter 2. In practice, so–called Hanbury Brown andTwiss experiments are performed to measure photon statistics [310]. We use abeam splitter and two detectors in lack of a detector without timing jitter anddead time. A typical setup for performing an auto–correlation measurementis shown in Figure 8.1 (a). Here, the filtered photons of the transition underinvestigation are split by a 50:50 beam splitter and detected by either oftwo detectors. The studied transition is filtered either via a transmissionspectrometer or by reflection on a volume Bragg grating. In auto–correlationmeasurements histograms are generated that disclose the difference in arrivaltimes between emitted photons. We use the home–built time tagging analysissoftware ETA [311] to evaluate the time–tagged data. Such a histogram isshown in Figure 8.1 (b) for the biexciton state of an InAs/GaAs quantum dotunder pulsed, two–photon resonant excitation. Since pulsed excitation is used,excitation of the quantum dot can only occur every 12.48 ns, which corresponds

57

58 8. Correlation spectroscopy measurements

Figure 8.1: (a) Schematic setup for a Hanbury Brown and Twiss measurement.The filtered photons are impinging on a 50:50 beam splitter and afterwardsdetected by either of two detectors, here illustrated by two fiber couplers thatare connected to two fiber–coupled detectors. The time of arrival of the detectedphotons are recorded by time–tagging electronics (not depicted). (b) Histogramobtained from an auto–correlation measurement performed on an InAs/GaAsquantum dot under pulsed two–photon resonant excitation.

to the repetition rate of the laser. In the histogram, the suppression of the peakat zero time delay is apparent. To evaluate the auto–correlation measurementsand determine the degree of second order coherence, the events in the peaks aresummed up (if there is no overlap between the side peaks, the full repetitionperiod of the laser can be used). The amount of events in the center peakis divided by the average of events in the side peaks, which determines thedegree of second order coherence. For the histogram in Figure 8.1 (b), a valueof g(2)(0) = 0.04± 0.01 is calculated. Here, no fitting (temporal postselection)and no background subtraction has been used. In the histogram, we observethat the peak area slightly decreases with larger time delay, which is related toblinking. This behavior is attributed to a shift of the two–photon resonance dueto changes in the charge environment of the quantum dot. A detailed model ofblinking is discussed by Jahn et al. [289].The first demonstration of single photon emission from a semiconductor quantumdot was presented by Michler et al. in 2000 [43] and has since then seen strongimprovements in terms of single photon purity. While initially non–resonantexcitation schemes were used which can lead to re–excitation of the quantum dotwithin the same excitation cycle [312], resonant excitation schemes that directlyaddress the quantum dots states lead to superior single photon purity [204],[205], [219], [220], [293], [301]. In Paper 1 we demonstrated how the excitondecay is shielding the biexciton level from re-excitation when using two–photonresonant excitation. The limitations of s–shell resonant excitation and two–photon resonant excitation in terms of possible single photon purity are discussed

8.2. Hong–Ou–Mandel experiments 59

in Paper 9. Furthermore, both sample quality and detector technology haveimproved, which is contributing to improvements in observed single purity.

8.2. Hong–Ou–Mandel experimentsFigure 8.2 shows a schematic of a setup used for a Hong–Ou–Mandel experimentto determine the two–photon interference visibility. In Fig. 8.2 (a) the delayline for the excitation laser is depicted which allows to generate double–pulseswith varying delay Δt, such that the fixed delay provided by the fiber–basedMach–Zehnder (see Fig. 8.2) is matched. Each excitation pulse from the laser issplit into two pulses, such that within every excitation period of 12.5 ns (basedon a repetition rate of 80MHz) the quantum dot is excited twice with a delayof 2 ns (Fig. 8.2 (b)). This generates two photons pearly and plate The quantumdot photons are spectrally filtered and then sent into the second Mach–Zehnderinterferometer. Here, the photons can take either the short path or the long pathwith additional delay Δt. The two outputs of the interferometer are connectedto superconducting single photon detectors. Depending on whether pearly orplate takes the short or long path, respectively, different coincidence eventsoccur, leading to a pattern of quintuplets, as shown in Figure 8.3. Here, thecenter quintuplet stems from coincidence events within the same excitation cycle,whereas the side quintuplet stems from photons from different excitation cycles.Following the labels in Fig. 8.3 (a), peaks 1 and 5 in the center quintupletstem from photons that have acquired the maximum temporal delay withinone excitation cycle in the second Mach–Zehnder interferometer. This is thecase, when pearly takes the short path and plate takes the long path, resultingin a temporal difference of 2Δt. If both pearly and plate end up taking the samepath, they will keep the temporal difference of Δt from the double excitationpulse and contribute to peaks 2 and 4. Since this can happen in the short andlong arm, the area of peak 2 and 4 is expected to be twice as large as of peaks1 and 5. Only photons that arrive at the second beam splitter at the sametime contribute to the center peak 3. This is the case when pearly takes thelong path and plate takes the short path. For indistinguishable photons thecenter peak then disappears, as discussed in Section 2.3. For distinguishablephotons, the area of the center peak would be the same as for peaks 2 and 4,as when the photons arrive at the same time at the second beam splitter thereare two possible coincidence events that contribute to the center peak (pearlyon detector 1 and plate and on detector 2 and vice versa). Overall, this resultsin a peak area ratio of 1:2:0:2:1 for indistinguishable photons and 1:2:2:2:1 fordistinguishable photons in the center quintuplet. In Figure 8.3 a histogramgenerated from a measurement of the biexciton state of a GaAs quantum dotunder two photon resonant excitation is shown with a zoom into the centerquintuplet in 8.3 (b). Here, a dip in the center peak can be observed. Forperfectly indistinguishable photons, the center peak would disappear completely.However, based on a theoretical analysis by Legero et al. [313], the dip existsbecause of inhomogeneous broadening of the photons and its width dependson the mutual coherence time of the photons [314]. In order to evaluate the


Figure 8.2: Setup schematic for Hong–Ou–Mandel type measurements (a) Laserdelay line for generation of laser double pulses with variable delay Δt. (b) Thelaser double pulses are used to consecutively excite the quantum dot within onelaser repetition cycle. (c) After filtering, the quantum dot photons are sent intoa fiber–based unbalanced Mach–Zehnder interferometer, where the interferenceis occurring on the second beam splitter.

Hong–Ou–Mandel visibility V from experimental data, the areas of peaks 2 and4 compared to the center peak are compared as follows [147]:

V =2A3

A2 +A4(8.1)

As discussed in the supplementary material of Paper 4, it is of crucial importanceto sum up the data within the peaks instead of integrating the peaks via fitsand to have a good enough setup time resolution to resolve the dip. Otherwise,the Hong–Ou–Mandel visibility can be overestimated.

8.3. Entanglement measurementsIn order to quantify the degree of entanglement of photons emitted from aquantum dot, polarization resolved cross–correlation measurements betweenthe filtered biexciton and exciton emission are performed. In Figure 8.5 (a) thesetup used for the polarization resolved correlation spectroscopy is depicted.The quantum dot photons and residual laser photons sent onto two Notch filters(NF) that are rotated such that they reflect either the biexciton or the excitonphotons. The quantum dot photons then pass a set of waveplates (λ/2 and λ/4)and a polarizer before being coupled into single mode optical fibers that lead to

8.3. Entanglement measurements 61

Figure 8.3: Measured two–photon interference data from a GaAs quantumdot biexciton under two–photon resonant excitation. (a) Measurement datashowing the center quintuplet and side quintuplets. (b) Zoom–in to the centerquintuplet revealing a dip in the center peak at zero time delay.

the detectors.Regular cross-correlation measurements are used to confirm that photons thatappear to originate from a biexciton–exciton decay are indeed correlated. Thephotons emitted by biexciton and exciton are spectrally separated from oneanother and sent to a detector each, while their arrival times are being recorded.The characteristic feature in a cross–correlation histogram for a cascade are adip at zero time delay followed by an asymmetric bunching peak that decayswith the lifetime of the exciton. First the biexciton is decaying, leading to anantibunching dip, as a finite time has to pass before the biexciton state can beexcited again. This is followed by the decay of the exciton, which is causingthe characteristic bunching signature, shown in Figure 8.4 (b). The data ofthe cross–correlation measurement is collected from a GaAs/AlAs quantum dotwith emission close to 795 nm that is excited via pulsed two–photon resonantexcitation.To reconstruct the density matrix and determine the degree of entanglementof photons emitted by a quantum dot, polarization resolved cross–correlationmeasurement between biexciton and exciton state are performed in 36 com-binations of linear, diagonal and circular basis. In Figure 8.4 (c), the centerpeak (light blue shaded area in Figure 8.4 (b)) is shown for two polarizationmeasurements HH and HV. Compared to the data in Figure 8.4 (b), oscillationsin the decay are visible, which are due to the time–evolving Bell state causedby the finestructure splitting of the quantum dot as discussed in Section 2.4.The finestructure splitting of this particular quantum dot was measured to be12.2μeV.


Figure 8.4: (a) Spectral filtering and polarization analysis setup for polarizationresolved cross–correlation measurements. The quantum dot photons are spec-trally filtered and separated via notch filters (NF) and can then be analyzed inpolarization with waveplates and polarizers. Dark blue open circles schemati-cally represent exciton photons, pink open circles the biexciton photons andgreen solid line the excitation laser pulses. (b) Non–polarization resolved cross–correlation measurement of the radiative cascade of a GaAs/AlAs quantum dot.The light blue shaded area indicates the temporal window that is shown in part(c). (c) Polarization–resolved measurements in HH and HV polarizations.

To determine the required waveplate angles, a setup as shown in Figure 8.5 (a)is used. Our pulsed laser (2 ps) that is spectrally broad enough to cover thebiexciton and exciton wavelength is coupled into the detection setup of Figure8.5 (a) with an additional mirror. An extra quarter and a half waveplate areused to set a specific input polarization of the laser, which is confirmed with apolarimeter. The polarimeter is then moved into the filtering arms of our setup


R

V

RRV

From Laser...(a)

NF

FCM

Pol

/2/4

BD Pol-M

HH

HV

VVV

H HH

VHHV

VV

Real part

HH

HV

VVV

H HH

VHHV

VV

Imaginary part

(b)

(c)

0.00

0.25

0.50

0.75

1.00

0.00

0.25

0.50

0.75

1.00

Figure 8.5: (a) Waveplate characterization setup to determine the waveplateangles for the quantum state tomography measurements. The laser is launchedinto the setup in the six polarizations (H, V, A, D, R, L) that are required forthe tomography measurement. The laser polarization is monitored with thepolarimeter. After reflection on the notch filter, the motorized waveplates areset up such that each of the six polarizations is turned to pass the polarizer(V), which is again confirmed with the polarimeter. (b) Real part of the densitymatrix reconstructed for incoming H polarized laser light. Blue bars correspondto positive values, pink bars to negative values and gray to zero. (c) Imaginarypart.

and placed after the two waveplates that are used for setting the polarizationof the quantum dot photons (indicated by the opaque polarimeter in Figure 8.5(a)). At this point, the second set of waveplates are set such that the laser inputpolarization is turned to the polarization transmitted by the polarizer. In otherwords: the studied polarization is always turned such that it is passing the


polarizer and can, thus, be detected. This is repeated for all 6 input polariza-tions and performed in both arms of the detection setup. The waveplate anglesdetermined in this way can be set automatically in the measurement. Thereconstructed density matrix for horizontally polarized laser pulses is shown inFigure 8.5 (b) and (c) both real and imaginary part. For the H polarized laser,correlations are expected only when both photons are measured with horizontalsettings. Here, we measure a fidelity of (99.747± 0.054)% to the state |HH〉.We repeat the procedure for incoming diagonally and right circularly polarizedlight and obtain a fidelity of (99.849± 0.025)% for the diagonal laser pulsesand (97.21± 0.25)% in case of the circular polarization. To analyze the data,we use the Optical Quantum State Tomography Code [315] that follows thedensity matrix reconstruction based on Ref. [316].After careful determination of the waveplate angles, 36 polarization resolvedcross–correlation measurements with the filtered quantum dot biexciton andexciton photons are performed. The fidelity of the quantum dot photons to theBell state Ψ+ is depicted in Figure 8.6 (a). The magnitude of the finestructuresplitting obtained from a polarization–dependent photoluminescence measure-ments fits well to the value obtained from the oscillation between the Bellstates of this measurement of 10.9μeV. The maximum obtained fidelity toΨ+ is (96.7± 0.8)%. The concurrence as a function of time delay is shown in

Figure 8.6: (a) Fidelity to the state Ψ+ as a function of time. (b) Concurrenceas a function of time. The data from 36 polarization resolved correlationmeasurements has been analyzed in 16 ps bins. The dark blue open circlesrepresent the data points, the light blue shaded areas represent the errors. Thegray area marks a time window before the rise of coincidences for negative timedelays (see also Figure 8.4 (c)).

Figure 8.6 (b), with a maximum value of (94.4± 0.9)%. It can be observed


that the concurrence follows a specific behavior, similar to the one discussedin Reference [237]. Here the authors describe how the sampling of the detec-tor response function influences the observable concurrence in the presence offinestructure splitting and a finite time resolution. In our case, the concurrenceexhibits a peak at 0 ns, which slightly goes down and reaches an almost flat levelbetween 0.2 ns to 1 ns, before dropping and becoming more noisy after 1 ns. Themaximum of the concurrence is observed, when the detector response starts tosample more and more correlation events and it goes down again once so manycorrelation events are sampled within the detector response that the averagingproperties the phase term in Equation 3.10 contributes increasingly. Eventually,as the whole detector response is sampling the evolving state, the concurrencereaches a flat level of around 0.8. Beyond 1 ns, the majority of quantum photonshas already decayed, hence the concurrence decreases and becomes noisy. Thisoverall behavior shows us that for the studied quantum dot with its givenfinestructure splitting a higher setup time resolution (compared to our ≈ 60 ps)would be beneficial. In Figure 8.7 the resulting density matrix reconstructed

Figure 8.7: Density matrix obtained via quantum state tomography for aresonantly excited GaAs/AlAs quantum dot. Blue bars correspond to valuesabove zero, pink bars to values below zero and gray areas represent zero. (a)Real part (b) Imaginary part.

from 36 polarization resolved cross-correlation measurements is presented withthe real part in Figure 8.7 (a) and the imaginary part in 8.7 (b). As expectedfor an entangled state, the density matrix exhibits nearly only outer-diagonalelements. All other elements are strongly suppressed showing that the emittedphoton pairs are in a non–separable and co–polarized state. In contrast, aseparable, classical state of the form Ψclass =

12 ((|H〉+ |V〉)⊗ (|H〉+ |V〉)) would

exhibit elements along the diagonal with height 0.25.

Chapter 9

Conclusions and outlook

In this thesis, we have studied, the use of semiconductor quantum dots assources of single and indistinguishable photons and entangled photon pairs withthe vision of making them applicable for quantum photonic applications. Wehave researched quantum dots with emission in the telecom range for future longdistance transmission of quantum bits in optical fibers, using self–assembledInAs/GaAs quantum dots and InAsP nanowire quantum dots. Droplet–etchedGaAs/AlAs quantum dots with emission close to the Rubidium D1–transitionhave been investigated, whose photons could couple to atomic transitions ofquantum memories to realize quantum repeaters.We have used non–resonant characterization techniques such as photolumines-cence mapping to extract the emission wavelengths, linewidth and quantumdot density by examining a large amount of quantum dots on a specific part ofa sample. Polarization–resolved photoluminescence measurements have beeninstrumental to determine the finestructure splittings of quantum dots underinvestigation and identify biexciton–exciton pairs for subsequent entanglementmeasurements. Time–resolved correlation spectroscopy has been an essentialtool to determine the decay times of semiconductor quantum dots, performantibunching and indistinguishability measurements, as well as (polarization–resolved) cross–correlation experiments.The following paragraphs will give a brief roundup of results achieved duringthe course of this PhD thesis, which are presented in Part II.

Telecom quantum dotsQuantum dots with emission in the telecom range have been investigated inPapers 2, 3, 5 and 8. Photons emitted by these kind of quantum dots are suitablefor generating quantum bits that can be transmitted over long distances in opti-cal fibers. In Paper 2, the emission of InAsP nanowire quantum dots is shiftedinto the telecom range by adjusting the quantum dot material composition andsubsequent tailoring of the nanowire diameter. These quantum dots have beenfabricated and optimized by our collaborators at NRC Canada in the group ofDan Dalacu and Philip J. Poole. We demonstrate single photon emission underpulsed non–resonant excitation and show that the decay times remain similarcompared to nanowire quantum dots with emission in the near–infrared.

66

9. Conclusions and outlook 67

A growth recipe for InAs/GaAs quantum dots with a metamorphic buffer layerand emission in the telecom C–band that was pioneered by the group of Prof.Peter Michler has been adapted for the epitaxy machine at KTH operated byMatthias Paul, Carl Reuterskiold Heldund, Carlos Nunez Lobato and MattiasHammar. With optical characterization measurements we have accompaniedthe growth processes until low density samples with low finestructure and emis-sion in the telecom C–band had been obtained. We have adjusted the layerthicknesses via a transfer matrix method. We have integrated these quantumdots onto piezo–electric substrates in Paper 3 via a versatile transfer techniquethat allows to integrate samples independent of their structure. In our case,we transferred a mechanically thinned sample with DBR mirrors. We havedemonstrated a highly stable emission wavelength of our tuned quantum dots.In Paper 5 we have generated single photons from an InAs/GaAs quantum dotand phase modulated them to generate frequency sidebands. We show that thesingle photon properties are preserved under this operation. Pulsed two–photonresonant excitation is used in Paper 8 to generate single photons on demand inthe telecom C–band with a biexciton lifetime below 500 ps. In addition, we usea phonon assisted TPE scheme to generate entangled photon pairs on–demandwith a concurrence of 91.4%.

GaAs quantum dotsGaAs/AlAs quantum dots with emission around 795 nm are the sources ofquantum states of light in Papers 1, 4, 6, 7 and 9. TPE has been usedin Paper 1 to generate single photons of unprecedented purity, yielding ag(2)(0) = (7.5± 1.6)× 10−5. This result is based on shielding of the biexcitonlevel from unintentional re–excitation by the exciton decay and the negligibledark counts of our detectors. We have applied the same excitation scheme to aquantum dot in a micro parabolic cavity in Paper 7 to generate piezo–tunablesingle photons. The broadband microstructure yields an average extractionefficiency enhancement of one order of magnitude while the simulated Gaussianemission profile should promote coupling into single mode optical fibers. More-over, we have generated entangled photon pairs from a GaAs/AlAs quantumdot and subsequently performed entanglement swapping which is reported inPaper 6. A theoretical model is developed to estimate the achievable swappingfidelity for a given quantum dot finestructure splitting and indistiguishability.We have generated indistinguishable photons under pulsed RF in Paper 4without using Purcell enhancement. Raw visibilities of up to (95.0+5.0

−6.1)% areobtained. In Paper 9, we have studied the limitations of using a three–levelsystem under two–photon resonant excitation versus a two–level system unders–shell resonant excitation for both single and indistinguishable photon gener-ation. Here, TPE yields superior results concerning the single photon purity,while the single purity observed under RF is limited by re–excitation. We showthat RF yields photons of higher indistinguishability from the same quantum

68 9. Conclusions and outlook

dot compared to TPE based on time jitter introduced by the radiative cascade.

Possible future workBased on the numerous results obtained during the course of this thesis, Ienvision a variety of future experiments. As discussed in Part I, resonantexcitation techniques are crucial to observe the best possible quality of single,indistinguishable and entangled photons, which is however at this point mostlydemonstrated with quantum dots in the near–infrared. At the time of writing,no Hong–Ou–Mandel experiments under pulsed, s–shell resonant excitation ofquantum dots in the telecom C–band or O–band have been demonstrated. Inthis context it would also be very interesting to study the indistinguishability ofnon–consecutive photons as discussed by Wang et al [317] and Loredo et al. [318]since this parameter directly influences the maximum achievable fidelities ofquantum operations e.g. when storage of photons and subsequent quantuminterference with other photons are taking place.The finestructure splitting of the InAs/GaAs quantum dots is on averagesufficiently low to perform entanglement measurements, however, integrationof these quantum dot devices in six–legged piezo device (see Reference [122])would allow to deterministically remove the finestructure splitting while alsocontrolling the emission wavelength. Spectral overlap is yet another step towardsscalability of quantum dot devices.Integration of semiconductor quantum dots into diode structures could reducethe quantum dot linewidth [319] by controlling the charge environment togenerate larger overlap of the quantum dot emission with atomic resonances,which would be of interest for all studied types of quantum dots.One major drawback of telecom quantum dots to date is their brightness. Ultrabright sources of single, indistinguishable and entangled photons have so farbeen mostly demonstrated in the near–infrared, see e.g. Papers by Liu et al. andWang et al. [219], [220]. Long distance and high key rate applications in quantumkey distribution and quantum communication require bright emitters [51] attelecom wavelengths, making (broadband) extraction efficiency enhancing microstructures a prerequisite. Ideally these micro structures engineer the biexciton’sand exciton’s lifetime to mediate the limit of indistinguishability obtainablevia the radiative cascade. A logical next step of the work carried out sofar would be to integrate telecom quantum dots into (positioned) parabolicmicrocavities. Also the fabrication of compact fiber–coupled emitters is animportant next step, as this would make quantum dot sources much moredeployable, especially in combination with integration into compact cryostatsas discussed in References [254], [256]. Brighter sources would moreover allowintegration of quantum dots into fiber–based infrastructure outside of the lab andenable future quantum key distribution experiments at least on a metropolitanscale. Quantum teleportation and entanglement swapping experiments shouldbe pursued more, especially with remote quantum dots to better mimic real lifeapplications with distributed sources in a network. In this context there has been

9. Conclusions and outlook 69

some interesting work looking into how imperfect properties can be mitigatedin quantum teleportation [320] by means of spectral filtering. Kupko et al. havelooked into how temporal filtering can be used in an implementation of the BB84protocol with a quantum dot in terms of increasing the signal to noise ratio andenhanced secure communication distance [321]. Vural et al. have studied howthe decoherence mechanisms in InGaAs quantum dots and their influence onindisitiguishability of (non–) consecutively emitted photons is relevant for bothexperiments with several remote quantum dots and experiments that requirehigh two–photon interference visibilities on longer timescales [322].With brighter quantum dots, we should be able to integrate single photons andentangled photon pairs into the infrastructure of our quantum link. A thirdnode is currently under development and a cryostat with SSPDs will be installedin the Ericsson lab in the fall of 2020. This should allow to perform QKD–typeof experiments in real deployed fiber in a metropolitan–sized testbed. Oncethe quantum dot single photons are launched into deployed fiber infrastructurepolarization stabilization will be required to counteract environmental influencesonto the sent polarization. First steps in this direction have already been takenin a master project here at KTH [323] and will undergo more testing andoptimization in the future. Work in this context has also been published inReferences by Xiang et al. and Schimpf et al. [27], [175].At the time of writing this thesis, investments from several nations, suchas the United States, Canada, the European Union, Germany, the UnitedKingdom, China, Japan and Australia [324]–[331] on the order of severalhundreds of millions to billions of Euros for the coming decade are beingdistributed. I am hopeful to see many exciting developments in the field ofquantum communication in the coming years including continuous improvementsof the quantum dot technology, integration of semiconductor quantum dotsinto real–life quantum networks, as well as storage and read–out of singleand entangled photons emitted by semiconductor quantum dots in quantummemories. While there are still many demanding experiments to be done andimprovements to be made, with the current pace of technological advancement, Iexpect semiconductor quantum dots will be amongst the key enabling quantumtechnologies.

Appendix A

Transmission spectrometers for highly efficientspectral filtering

In order to be able to perform (cross–) correlation measurements at the singlephoton level, optical filtering systems are required. These should fulfill a fewcharacteristics, such as: high throughput, ideally fiber–based for easy connectionto single photon detection or optical fibers to connect to other experiments,narrowband filtering and flat response to different polarizations. To complywith these constraints, we have designed and built two transmission spectrome-ters (one for the telecom range around 1550 nm and one for the near–infraredrange around 795 nm). Using a transmission grating compared to a reflectivegrating as in our commercial spectrometers has the advantage of providing ahigh transmission through the grating [332], [333], while being considerably lesssensitive to the polarization [334]. Furthermore, while splitting the quantum dotsignal on a 50:50 beam splitter and filtering each transition line in a separatespectrometer, has been used successfully used to measure cross–correlations,it means sacrificing 50% of the photons. Achieving a suitable resolution toseparate different emission lines of a quantum dot or the excitation laser from aquantum dot emission line, is enabled by using a grating with a large numberof lines per millimeter and a big illuminating spot diameter on the grating.For the transmission spectrometer at telecom wavelengths, we select a trans-mission grating with 940 lines/mm (by the company Lightsmyth) and selecta beam diameter of 16mm at 1550 nm on the grating. For the near–infraredrange, we select a grating with 1503 lines/mm and a beam diameter of 15mmat 795 nm. The setup is shown below in Figure A.1. The beam diameter thatis illuminating the grating is given by the diameter of the input fiber collimatorC1 and the ratio of focal length of the lens L1 and the spherical mirror M1. Theentrance of the transmission spectrometer is the single–mode fiber connected toC1. Here, collimated light exits into free space. L1 has a with focal length of300mm. Together with M1 (focal length of fM1 = 1m) the two elements form atelescope and generate a larger collimated beam at the grating. A 1” mirror isadded, such that two mirrors are available to make the beam straight before thegrating. Both spherical mirrors require an angle of incidence of no larger than15◦, hence the steep angles in the triangles ∠ m1, M1, G and ∠ G, M2, m2. Ifthis angle is not satisfied, aberrations like coma occur, just like for using lenses.

70

A. Transmission spectrometers for highly efficient spectral filtering 71

Figure A.1: Photograph of a home–built transmission spectrometer. C: fibercollimator, L, lens, m: 1” mirror, M spherical 2” mirror (M2 is not shown), G:transmission grating, D: d-shaped mirror. The pink and blue lines representthe beam path that light at two different wavelengths takes through the opticalsystem.

By using curved mirrors instead of lenses, chromatic shifts of the focal pointcan be avoided compared to lenses. When using a different input wavelength,only L1 (and subsequently L2 and L3) needs to be shifted such that the focalpoint coincides again with fM1, or fM2, respectively. The transmission gratingis operated in a so–called Littrow–configuration, where angle of incidence anddiffraction angle are almost the same. In this configuration, the grating yieldsthe largest transmission efficiency. After passing the grating a second sphericalmirror is used, this time the mirror is focusing the beam down. Via the mirrorsm2 and m3, the beam is coupled into the fiber connected to C2. Two lenses(L2) are used in order to match the beam diameter to the fiber collimator. Asecond wavelength (e.g. a second quantum dot emission line, indicated by theblue lines in Figure A.1) can be picked up with a d–shaped mirror (D) in thefocal plane of M2 (fM2 = 1m). Here, the spatial separation translates to thespectral separation via:

∂x∂λ

= fM2g

cos(β). (A.1)

A spectral distance of 1 nm would correspond to a spatial separation of 2mmfor an incidence angle of β = 42◦ on the NIR grating with g=1503 lines/mm,and 1.39mm for the telecom grating with incidence angle of 48◦. For typicalspectral separations of biexciton and exciton that we observed in the GaAs

72 A. Transmission spectrometers for highly efficient spectral filtering

(InAs) quantum dots of 2.5 nm (4 nm), we achieve a spatial separation in thefocal point of M2 of 5mm (5.6mm). With such a separation, it is not demandingto pick up one of the two spectral lines with the d-shaped mirror. The sphericalmirror M2 and the lenses L2 or L3 in the two output arms form another telescope,to reduce the beam diameter again and collimate the light for fiber couplingto C2 and C3. Between fM1–M1, M1–G, G–M2 and M2–fM2 4f distances arekept in order to reduce aberrations. In Table A.1 the transmission of the usedcomponents are listed. For arm 1, we obtain a transmission based on these

Component Transmission Number of component insetup

Lens 0.99 3 in arm 1, 2 in arm 21”Mirror 0.97 3 in arm 1, 4 in arm 2

2” Sphericalmirror 0.96 2Grating 0.93 1

Table A.1: Optical components used a transmission spectrometer, transmissionvalues are given for a wavelength of 800 nm.

components of 75.9%, for arm 2 a transmission of 74.4%. We still have toaccount for the fiber coupling efficiencies, which are measured to be above80%, thus yielding a total system efficiency of 60.7% and 59.5%, respectively.For our experiments, an important design constraint was the bandpass of thespectrometer, which characterizes the full width at half maximum of the lightat the exit slit, which is in our case the spectral bandwidth of the light couplinginto the output fibers at C2 and C3. The bandpass Δλ is defined as:

Δλ =λ

g · d , (A.2)

with λ the center wavelength, and d the diameter of the spot on the grating.Here, we obtain 0.035 nm = 16.6GHz in the NIR spectrometer and 0.10 nm =12.8GHz in the telecom spectrometer. To confirm these theoretical values, weperform measurements with a tunable narrowband cw–laser, see also Figure A.2for the telecom spectrometer. Here, we measure a bandpass of 19GHz in theNIR spectrometer and 13GHz in the telecom one. These bandpasses fit wellwith the linewidths of our quantum dots discussed in Sections 6.1 and 6.3.

A. Transmission spectrometers for highly efficient spectral filtering 73

0.00 0.04 0.08-0.04-0.08

E (meV)

0.0

3.5

7.0P

ower

(μ

W)

Data

Gaussian fit

Figure A.2: Transmission into C2 fiber for fixed grating position measured witha tunable narrowband laser.

Appendix B

Finestructure optimization of InAs/GaAsquantum dots

After optimizing the growth of our InAs/GaAs quantum dots on a metamorphicbuffer to achieve emission in the telecom C–band and optized DBR reflectivities,we started to look for a quantum dot with biexciton–exciton cascade and lowfinestructure splitting. At this point, we discovered that the finestructureaverage finestructure splitting of the quantum dots on this sample (see FigureB.1 (b), with a growth temperature of 530 °C and average FSS of 25μeV) waslarger than what we could afford with the given time resolution of our setup.In the telecom range, our setup time resolution is approximately 70 ps. Basedon this, we were aiming to find a QD with finestructure splitting below 10μeV.This FSS corresponds to an oscillation between the Bell states of ≈415 ps,meaning that per oscillation period, we would find 6 data points to reconstructthe oscillation. A smaller FSS would of course be advantageous. In order toinfluence the average FSS, the team of Mattias Hammar changed the growthtemperature of the quantum dots. Our observations based on measuring thefinestructure splittings of at least 25 quantum dots per sample at 4 differentgrowth temperatures is presented in Figure B.1. The lowest average FSS isfound for growth at 545 °C (see B.1 (c), (d), and (e)). For this temperaturewe compare quantum dots at the sample edge, the sample center and on adifferent sample with same growth temperature and a DBR mirror underneaththe QDs. In all three cases, the average FSS is lower compared to lower growthtemperatures or higher growth temperatures. This could be attributed to thefollowing: While the average FSS in Figure B.1 (a) and (b) is the same withinthe error, a temperature increase to 545 °C yields a lower observed FSS, whichcould be attributed to more symmetric quantum dots based on an increaseddiffusion length. With we even higher growth temperature, the mobility duringthe growth process is increased more and results in fewer, but enlarged quantumdots [335]. Larger quantum dots on the other hand are more subject to onaverage larger finestructure splittings, as observed e.g. by Tartakovskii etal [336] and Seguin et al. [337]. The authors attribute this to piezoelectricitywhich is increased with quantum dot size based on the lattice mismatch ofInAs QDs and GaAs substrate. While we have identified an optimal growthtemperature to produce QDs with emission in the telecom C–band and low FSS,

74

B. Finestructure optimization of InAs/GaAs quantum dots 75

a more thorough study of the growth processes and the resulting average FSSincluding more growth temperatures, and more studied QDs to obtain betterstatistics, could yield intersting insights into the growth dynamics of InAs QDson metamorphic buffers.

Figure B.1: Mean FSS for varied QD growth temperature. (a) Δ = 19.88μeV,27 QDs measured. (b) Δ = 24.15μeV, 26 QDs measured. (c) Δ = 9.05μeV,26 QDs measured at the sample edge. (d) Δ = 11.66μeV, 39 QDs measuredat the sample center of sample (c). (e) Δ = 6.0μeV, 33 QDs measured on asample with identical growth temperature as in (c) and (d), but with additionalDBR. (e) Δ = 16.79μeV, 35 QDs measured.

Appendix C

The Stockholm quantum link

In this chapter I will discuss the deployed fiber link that extends betweenthe QNP lab at KTH, Ericsson research lab in Kista and Telenorr researchLab in Solna. The link extends over a length of 20.2 km between KTH andEricsson, 17.15 km between KTH and Telenorr and 17.03 km between Ericssonand Telenorr. The link consists to a large extend of fiber that belongs tothe Stockholm metropolitan fiber network provided by Stokab. An artisticsketch of the fiber link is shown in Figure C.1. The purpose of this link is tostudy polarization behavior in deployed fiber, how experiments in deployedfiber differ from experiments with spooled fibers and what obstacles arise whenwe try to integrate our sources of quantum light into such a classical network.Eventually, the purpose is also to use it for QKD experiments with quantumdots in deployed fiber. In the following I will list the properties of the fiber anddiscuss preliminary experiments that have been carried out so far.

C.1. Link propertiesIn table C.1, the properties of the fiber link at the time of writing are listed.It can be seen that the fiber losses are higher than the expected 0.2 dBkm−1

at 1550 nm, with at most 0.48 dBkm−1. This is because the fibers are notspliced, meaning that there are some physical fiber–to–fiber connections andthe fibers have aged due to environmental influences. With the cryostat locatedin the QNP lab for the generation of single and entangled photons, the photonsexperience at most a loss 8.37 dB, which corresponds to a transmission of 14.5%of the photons from sender to receiver. During first measurements with alooped fiber between QNP lab – Ericsson research lab – QNP lab, we havediscovered two properties of the link that need to be taken care of beforemeasurements with quantum dot single and entangled photons.On the one hand, the dark fiber provided by Stokab is not completely freeof background photons that can be detected by our superconducting singlephoton detectors. Even without sending any single photons, we observe a levelof approximately 9000 cts/s (of which 30 cts/s are detector dark counts) byconnecting the looped fiber to the detector. Attempts to record spectra of thesephotons have not yielded insights into the spectral distribution of the photons.With our InGaAs array, integration times of longer than 60 s are not possibleas the array will saturate with background noise. For integration times up to

76

C.1. Link properties 77

Figure C.1: Artistic view of the Stockholm quantum network with photongeneration in the QNP lab at KTH Stockholm and photon detection in EricssonResearch Lab in Kista and Telenorr Lab in Solna.

Connection between Length (km) Loss (dB) ConnectionsQNP (Ch1) → Ericsson (Ch029) 20.2 7.8 2QNP (Ch2) → Ericsson (Ch030) 20.2 8.37 2QNP (Ch3) → Telenorr (Ch045) 17.15 7.92 2QNP (Ch4) → Telenorr (Ch046) 17.15 8.31 2Ericsson → Telenorr (Ch055) 17.03 5.34 2Ericsson → Telenorr (Ch056) 17.03 5.53 2

Table C.1: Quantum link deployed fiber properties including fiber lengths,measured losses and number of connections.

60 s, we can not identify a contribution in the spectrum (in a wavelength rangebetween 600 nm to 1600 nm) that could cause these observed counts. Since theobserved spectrum is flat, we assume that counts observed with the SSPD isa spectrally broad(er) signal or contributions from various wavelengths bands.This could be attributed to either room light in the connection rooms (which ishowever rather unlikely, as the visible light would not travel far and the fibercables are well shielded) or cross–talk from classical signals in the same fiber

78 C. The Stockholm quantum link

bundle.The dark fiber signal is also visible in a lifetime measurement that we performedwithin via the looped fiber, which is shown in Figure C.2 (a). Here, it contributesto the background below the actual quantum dot lifetime measurement anddominates the histogram. As it is flat also in time, we can conclude that it isnot correlated in time to our measurement performed at 80MHz or might stemfrom pulses in neighboring fibers that are interlaced in time. Investigations intowhere this signal comes from should be undertaken in the future. In Figure C.2(b), a comparison between the lifetime measured without the fiber (light greensolid line) and the data shown in C.2(a) with removed background (blue opencircles) is given. Within the fit error both lifetimes are the same and amountto 500 ps. While the origin of the dark fiber signal is still under investigation,

Figure C.2: (a) Lifetime measurement via looped fiber with photon generationand detection in the QNP lab at KTH. (b) Blue open circles: lifetime mea-surement from (a) with removed background and normalization. Green line:Lifetime measurement without any additional fiber.

the signal can spectrally be filtered strongly in a simple setup. We use a setupsimilar to the one in Figure 8.4 (a) to filter the signal containing both thedark signal and the quantum dot photons by reflecting it on a notch filter.In this way, the dark fiber signal can be reduced from 9000 cts/s to 100 cts/s.Beyond this, we have observed that if we transmit a defined polarization fromthe QNP lab through the fiber link to Ericsson lab, it will no stay constantover time. This is to be expected, as the fiber is not polarization maintainingand temperature drifts can influence the birefringence of the fiber over timeand, thus, change the received polarization. A measurement of the polarizationreceived in the Ericsson lab over 20 h is presented in Figure C.3. In C.3 (a) theStokes parameters as a function of time are shown. While there are no fastfluctuations of the polarization, there is a slight drift over time. We have also

C.1. Link properties 79

Figure C.3: (a) Evolution of the normalized Stokes parameters along the fiberlink during a period of 20h as a function of time. The data was recorded onbetween May 17th and May 18th 2020. H polarization is sent from the QNPlab to Ericsson lab and measured there with a polarimeter. (b) Evolution of thenormalized Stokes parameters on the Poincare sphere. The data was recordedduring a period of 5 days in May 2020.

observed, that if the fiber is touched in either of the labs, faster and strongerchanges of the polarization occur. Figure C.3 (b) shows the Stokes parametersas well, but this time plotted on the Poincare sphere to give a more illustrativeunderstanding of how much the polarization is changing over 20 h. While theobserved drift in polarization is slow and quantitatively small, a setup forpolarization control will be required for long measurements and is a work inprogress at the time of writing this thesis. First developments are summarizedin Reference [323].

Acknowledgements

Love, spread it like butter.

This thesis concludes a five year PhD project that started in an almostempty optics lab. During this time, countless samples from our collaboratorshave been studied, setups have been built, improved and torn down again.Papers have been written and friendships have been formed that hopefully lastmuch longer than these five years. While I have written this thesis by myself, Icould not have done it without the contribution and support of many absolutelyoutstanding people.First and foremost, I would like to thank my supervisor Prof. Val Zwiller forwelcoming me to the Quantum Nano Photonics group and providing a roofunder which we could build the lab and develop our ideas! Thank you for thefreedom you have given me to follow my path.I would like to thank my co–supervisor Prof. Klaus Jons for the continuoussupport and encouragements! Thank you for the brilliant supervision, for lettingme be a part of so many exciting experiments and for supporting me in stickingwith the dark telecom world! I only wish we could have baked even more piestogether in the last five years!Next, I would like to express my gratitude to the quantum dot growth team atKTH consisting of Prof. Mattias Hammar, Carl Reuterskiold Hedlund and Dr.Matthias Paul in the early days. Thank you for your interest in the project andproviding us with these amazing samples that made all the experiment possible!A special thanks goes to Matthias for joining us in Stockholm and helping usto get the telecom project started with your famous recipe.A big thank you goes to my team mates in the PhD office. I’m so gladthat we shared large bits of the strenuous path towards the PhD. Thanks forhelping out in the lab, supporting one another and being kind and fun officecolleagues. Julien, you have been around since day one and I’m so grateful foryour enthusiasm and everlasting kindness. Thomas, thank you for your helpon countless LabView emergencies, your nanofabrication skills and sharing mypassion for bread. I would like to thank Samuel for joining the telecom team,and making every day brighter with your eternal optimism. And finally Eva,I’m so glad we could share another part of the way as PhDs and share somesporty and food related adventures on the side.

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Acknowledgements 81

I would like to thank my fellow QNP colleagues Ali, Art, Carlos E.H., Lily,Marijn, and Mikael for many insightful discussions, fun coffee breaks and supportwhenever needed. You guys are a terrific team and I wish you all the best forthe future! Also a big thank you to our bachelor, KEX, master and projectstudents: Andrea, Ebba & Hilda, Julia & Linnea, Nicolas, Sandra, Selim, andUlrika. Martin och Theodor, tack for hjalpen med att oversatta det svenskaabstraktet. Stephan, I would like to thank you deeply for the endless hours youspent at the SEM to identify layers without any contrast and being such a funperson to spend time with inside and outside of Albanova!A huge thank you goes out to the quantum dot growers that provided uswith such excellent samples: the teams of Dan Dalacu and Philip Poole forthe nanowire quantum dots, Armando Rastellis group for the GaAs dropletquantum dots and as previously mentioned the KTH quantum dot growth team.You literally made my days in the optics lab brighter.Many collaborations have taken place during my PhD and have shown me thatteam work makes the Dream work! I am very grateful to have connected withsuch fun and knowledgeable people who made working long days and nightsmeaningful and pleasant. Together we have made a lot happen and I am verygrateful for the scientific community that has connected us. I would like tothank our collaborators from Munich, especially Lukas Hanschke, FriedrichSbresny and Kai Muller for your endurance, efforts and wisdom. A big thanksgoes also to the teams of Eden Figueroa and Patrick Ledingham. My thanksgoes to Oskars Oszolins for joining our efforts in the telecom range, and GemmaVall—Llosera for contributing a fresh perspective on quantum communicationincluding your absolutely contagious buzz. Last but not least, to the Minionsin Rome: Grazie dal profondo del mio cuore: Christian, Davide, Francesco,Michele and Rinaldo. Thank you all for your kindness and hospitality! I learnedso much while working with you.During my time at KTH I had the pleasure of co–supervising three masterstudents. I was lucky to have great supervisors along my academic path and hopeI could pass some of my experience on to you, Carlos, Kai and Liselott! Thanksfor your hard work on quantum dot growth, characterization and polarizationstabilization!I’m glad to have been a part of the PhD council in Applied Physics and theSCI school, the OSA chapter at KTH and the female network of ADOPT.A shoutout goes to all the people who keep Albanova running so smoothly andsupported us during our daily endeavors, namely Rolf’s workshop team whomade our wildest custom setup dreams come alive, the Godsmottagning teamfor supporting our mad ordering habits especially in the early days, our lovelydepartment administrator Madeleine for being a supportive ray of sunshineevery single day and finally Viktoria for building a gym that got me strong andlet me blow of steam in stressful phases.With my move to the North, I was fortunate enough to connect with someterrific people who have lightened up my days inside and outside of Albanova.I’m so grateful for having met all of you! Janosch & Selina, thanks for all the

82 Acknowledgements

good times! Sushi without wasabi and you? Nej, tack!! Francisca & Julien, it’slovely to have you around again and share another bit of the journey. Eleonora,I’m glad to have found another human who shares my passion for food and whoalways had a sympathetic ear during our time in Albanova! A big thanks toAmin for your kindness and friendship and many fun game nights.To my friends from home who have been close despite the distance: thankyou all for your everlasting support, long video calls and visits. I’m so gladwe made this work and to have you in my life! Marc, I’m grateful for yourregular cheer—ups and remote workouts during Covid! All the best for yournew career, you got this! To my study buddies, I’m super glad we’re all still intouch, Clarissa, Joni, Marco, Matze, Ting and Tobi! Melli, thanks so much forall the long phone calls and visits, I’m blessed to have you in my life!Mimi, my best friend for as long as I can remember. Thank you for alwayssupporting and motivating me, your love from near and far! It’s invaluable tohave a friend like you!I would like to thank my family for their everlasting love and support. Withoutyou I could not have done it!And finally, Lucas, thank you for having shared this journey with me. Thankyou so much for your loving support during long days, your everlasting patienceand optimism. I’m infinitely grateful to have found you.

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