Quantum dots and

entanglement

Tobias Huber

Thanks to…

Uni InnsbruckInstitute for exp. physicsGregor WeihsAna PredojevićMax PrilmüllerStephanie GrabherDaniel FögerHarishankar JayakumarThomas KautenMichael Sehner

Uni InnsbruckInstitute for theo. physicsHelmut RitschLaurin OstermannHashem Zoubi

Uni InnsbruckStaffCarina-Theresa OberhölerArmin SailerChristoph WegscheiderAnton SchönherrJQI @ NIST & UMD

Glenn Solomon

Uni StuttgartMarkus MüllerPeter Michler

Uni WaterlooMilad KoshnegarHamed Majedi

Uni BordeauxPhilippe TamaratBrahim Louis

Uni OlomoucIvo StrakaMiroslav JežekRadim Filip

CNRC CanadaDan DalacuPhilip Poole

Uni WürzburgChristian SchneiderSven Höfling

Why care about quantum light?

www.scienceabc.com www.ligo.caltech.edu/page/ligo-detectors

Communication Interferometry Imaging

www.rp-photonics.com

J. Carolan et al. Science

youtube.com, NIST

Optical quantum computing Metrology Fundamental new physics

sciencealert.com

Outline• Quantum dots (QD)

• (Two photon) entanglement• Polarization entangled photons

• Time-bin entangled photons

• 2 photon resonant excitation

• Hyper-entanglement

Quantum dots

• Semiconductor structure

• confined in all 3 dimensions

©JQI

Bryant and Solomon,

Optics of quantum dots and wires, 2005

Bryant and Solomon, Optics of quantum dots and wires, 2005

Electronic structure:

Confined states:X – ExcitonXX – BiexcitonX+(-) – Charged exciton (trion)XX+(-) – Charged biexciton

Excitation process:

Quantum dot states

Entanglement

• 2-qubit entanglement:

𝜓 𝐴𝐵 ≠ 𝜓 𝐴⨂ 𝜓 𝐵

4 Bell states, e.g. :

𝜙+ = 1

20 𝐴⨂ 0 𝐵 + 1 𝐴⨂ 1 𝐵

= 1

2( 00 + |11⟩)

Polarization entanglement from QDs

𝜙 = 1

2( 𝐻𝐻 + 𝑒𝑖𝑆𝑡/ℏ|𝑉𝑉⟩)

Minimize S by:• Finding a round quantum dot• E-field (Gerardot et al. APL 90, 041101 (2007),

Muller et al. PRL 103, 217402 (2009))

• B-field (Kowalik et al. PRB 75, 195340 (2007)

• Strain (Trotta et al. PRB 88, 155312 (2013)

• Thermal annealing (Ellis et al. APL 90, 011907

(2007))

• Fine-structure splitting S must be small• or fast detection to resolve phase change

H … horizontally polarized photonV … vertically polarized photon

Reconstructed density matrix

Experiment Theory

Fidelity F=0.81(6)Concurrence C=0.71(5)

𝜌 = 𝜓 ⟨𝜓|Polarization entanglement

Time-bin entanglement

𝜓 =1

2𝑒𝑎𝑟𝑙𝑦 𝑋 𝑒𝑎𝑟𝑙𝑦 𝑋𝑋 + 𝑒𝑖𝜙𝑝 𝑙𝑎𝑡𝑒 𝑋 𝑙𝑎𝑡𝑒 𝑋𝑋

Pump interferometer phase 𝜙𝑝

is encoded into the state

Conventional excitation method

is not phase preserving

Resonant excitation necessary

2 photon resonant excitation of the biexciton

biexciton has 𝑀 = 0ground state has M = 0photon has 𝑆 = ±1 ground to biexciton state is (dipole)forbidden

𝐻 = 12Ω(𝑡)(|𝑔⟩⟨𝑥|+|𝑥⟩⟨𝑏|+𝐻.𝑐.+(Δ𝑥−Δ𝑏)|𝑥⟩⟨𝑥|−2Δ𝑏|𝑏⟩⟨𝑏|

Jayakumar et al. Phys. Rev. Lett. 110, 135505 (2013)Huber et al. Phys. Rev. B 93, 201301(R) (2016)

Resonant excitation allowsto create time bin entangledphtons

Reconstructed density matrix

ExperimentTheory

Fidelity F=0.87(4)Concurrence C=0.76(8)

𝜌 = 𝜓 ⟨𝜓|Time-bin entanglement

2 photon resonant excitation• What is it good for?

• deterministic generation of photon pairs Jayakumar et al. Phys. Rev. Lett. 110, 135505 (2013)

• improved indistinguishabilityindistinguishability improves from 0 to 0.39 Huber et al. New J. Phys. 17 123025 (2015)

• coherent controlenables e.g. creation of time bin entangled photons Jayakumar et al. Nature Communications 5, 4251 (2014)

• improved polarization entanglement fidelity improves from 0.72 to 0.81 Müller et al. Nature Photonics 8, 224–228 (2014)

Hyper-entanglement

• Entanglement in two (or more) degrees of freedom

𝜓𝐻𝑦𝑝𝑒𝑟 = 12|𝜓𝑃𝑜𝑙𝑎𝑟𝑖𝑧𝑎𝑡𝑖𝑜𝑛⟩⨂ 𝜓𝑇𝑖𝑚𝑒−𝑏𝑖𝑛

= 12𝐻1𝐻2 + 𝑉1𝑉2 ⊗ ( 𝑒𝑎𝑟𝑙𝑦1𝑒𝑎𝑟𝑙𝑦2 + |𝑙𝑎𝑡𝑒1𝑙𝑎𝑡𝑒2⟩)

• Good for: complete Bell state measurments, superdense coding,

enhanced noise robustness

Hyper-entanglement analysis• Tomographic reconstruction

• For n-qubit tomography:• 4𝑛 parameters are needed

• For a 2x2-qubit hyper-entangled state:• 256 different projections

• Subspaces can be selected:• Neglect projections in the other subspace

• e.g. 𝐻𝐻 = σ𝑖,𝑗∈𝑒𝑎𝑟𝑙𝑦,𝑙𝑎𝑡𝑒 |𝐻𝐻𝑖𝑗⟩

Analysis II and setup

Phase settings:𝜙𝑋(𝑋𝑋) = 0° … +𝑋

𝜙𝑋(𝑋𝑋) = 90° … +𝑌

Full hyper-entangled matrixFull reconstruction

Theory

Fidelity F=0.55(4)

𝜌𝑝𝑜𝑙 ⊗𝜌𝑡𝑖𝑚𝑒−𝑏𝑖𝑛

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