LETTERS

Ultrabright source of entangled photon pairsAdrien Dousse1, Jan Suffczynski1{, Alexios Beveratos1, Olivier Krebs1, Aristide Lemaıtre1, Isabelle Sagnes1,Jacqueline Bloch1, Paul Voisin1 & Pascale Senellart1

A source of triggered entangled photon pairs is a key component inquantum information science1; it is needed to implement functionssuch as linear quantum computation2, entanglement swapping3 andquantum teleportation4. Generation of polarization entangledphoton pairs can be obtained through parametric conversion innonlinear optical media5–7 or by making use of the radiative decayof two electron–hole pairs trapped in a semiconductor quantumdot8–11. Today, these sources operate at a very low rate, below 0.01photon pairs per excitation pulse, which strongly limits their appli-cations. For systems based on parametric conversion, this low rateis intrinsically due to the Poissonian statistics of the source12.Conversely, a quantum dot can emit a single pair of entangledphotons with a probability near unity but suffers from a naturallyvery low extraction efficiency. Here we show that this drawback canbe overcome by coupling an optical cavity in the form of a ‘photonicmolecule’13 to a single quantum dot. Two coupled identical pillars—the photonic molecule—were etched in a semiconductor planarmicrocavity, using an optical lithography method14 that ensures adeterministic coupling to the biexciton and exciton energy states ofa pre-selected quantum dot. The Purcell effect ensures that mostentangled photon pairs are emitted into two cavity modes, whileimproving the indistinguishability of the two optical recombina-tion paths15,16. A polarization entangled photon pair rate of 0.12 perexcitation pulse (with a concurrence of 0.34) is collected in the firstlens. Our results open the way towards the fabrication of solid statetriggered sources of entangled photon pairs, with an overall (cre-ation and collection) efficiency of 80%.

To date, most quantum information and communication protocolsnecessitating entangled photon pairs have been realized using sourcesbased on parametric down-conversion2–7. These sources presentPoissonian statistics: the probability that each pulse contains two pairsis half the squared probability of containing only one. As the fidelity ofthe protocol is degraded with increasing two-pair probability12, theaverage photon pair per pulse has to be typically limited to 0.05.Recently, it has been shown that a single semiconductor quantumdot can emit polarization entangled photon pairs8–11. Two electron–hole pairs (a biexciton, called here the XX state) trapped in a quantumdot recombine radiatively through a two-photon cascade. As shownschematically in Fig. 1a, two radiative recombination paths are pos-sible through two exciton (X) states of orthogonal polarization. If thetwo X states are degenerate (anisotropic exchange splitting S 5 0), thetwo recombination paths are indistinguishable and the pair of emittedphotons is polarization entangled17. For excitation powers saturatingthe XX transition, we can ensure that one photon pair is emitted foreach excitation pulse. However, in bulk material, less than 2% of thepairs can be collected as they are emitted isotropically in a high refrac-tive index material.

To collect the emitted photons, the quantum dot spontaneous emis-sion can be controlled and funnelled into an optical cavity mode18.When a quantum dot is spatially and spectrally coupled to a cavity

mode, its emission rate into the mode is increased by the Purcell factorFp, and a fraction Fp/(Fp 1 1) of the quantum dot emission is funnelledinto the mode. Single photon sources with an overall efficiency around38% have been realized following this scheme19. However, imple-mentation of the same concepts to extract polarization entangledphoton pairs is not straightforward. First, X and XX photons are emit-ted with an energy difference that usually strongly exceeds the width ofa single cavity resonance. Moreover, the coupling to the optical modemust be independent of the polarization for both emitted photons, asan increased Purcell factor for one recombination path would lead tothe generation of non-maximally entangled states. Finally, the radi-ation pattern of the optical modes should not depend on polarization,in order to ensure that no ‘which-path’ information can be obtainedthrough the knowledge of the photon emission angle20.

In the present work, we fabricate an ultrabright source of entangledphoton pairs by deterministically coupling a quantum dot to a photonic

1Laboratoire de Photonique et de Nanostructures, CNRS, route de Nozay, 91460 Marcoussis, France. {Present address: Institute of Experimental Physics, University of Warsaw, 69Hoz

.a Street, 00-681 Warsaw, Poland.

Energy

Ene

rgy

(meV

)

M4–5

M3

M2

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M1

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zy

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1,346

1,344

|XX⟩

|X⟩ S

|0⟩

a

b c

Figure 1 | Principle of photon extraction using a photonic molecule.a, Sketch of the radiative cascade in a single quantum dot. See main text fornomenclature. b, Diagram of the source: two identical pillar microcavitieswith diameter D are coupled. The centre to centre distance is labelled CC9. Asingle quantum dot (QD) is inserted in one of the pillars. k is the photonwave vector. c, Energy of the optical mode of the photonic molecule forD 5 3 mm and various centre to centre distances. The molecule modes arelabelled M1–M5. Dashed lines are guides to the eye.

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217Macmillan Publishers Limited. All rights reserved©2010

molecule. To obtain two cavity resonances for both XX and X photons,the quantum dot is inserted in a micropillar cavity coupled to a secondidentical but empty micropillar (Fig. 1b). The mode energies of thesephotonic molecules are presented in Fig. 1c, for an individual pillardiameter D 5 3mm and a set of centre-to-centre distances, CC9.Reducing the distance CC9 leads to a coupling of the individual pillarmodes, resulting in a splitting of each mode. By choosing pillar dia-meter D and distance CC9, it is therefore possible to independently tunethe energies of the photonic molecule modes (M1–M5) and the energydifferences between them to match both X and XX energies. Figure 2shows that, despite the reduction of symmetry, the properties of themolecule’s optical modes are independent of their polarizations over alarge range of parameters. Each mode (M1–M5) of the photonic mole-cule presents a polarization splitting of only few tens of microelectronvolts (Fig. 2a). To measure such small polarization splittings, moleculeshave been fabricated on a high-quality-factor (Q 5 60,000) calibrationsample. For a microcavity of moderate quality factor (Q 5 4,500, modelinewidth around 300meV), this small splitting ensures a strong spectraloverlap of the modes both in H (horizontal) and V (vertical) polariza-tions, needed to achieve a polarization independent Purcell effect.Similarly, Fig. 2b shows radiation patterns measured on photonic mole-cule A with D 5 2.4mm and CC9 5 1.8mm: the radiation patterns of themodes M1–M3 are identical in H and V polarization (overlap .98%).

Photonic molecules deterministically coupled to a single quantumdot are fabricated using low temperature in situ photolithography21 ona planar microcavity in which a quantum dot layer is embedded, asdescribed in ref. 14. Two disks are exposed in the resist to define thephotonic molecule, with the quantum dot located at the centre of onepillar. To emit polarization entangled photons, S must be smaller thanthe X homogeneous linewidth17. Annealing22 the sample reduced S to1–4meV. Several molecules operating as sources of entangled photonpairs between 5 K and 52 K were fabricated in one process. We reportthe emission properties of molecule B, for which the X line is resonantto mode 3, and the XX line is resonant to mode 2 at 5 K. This spectralmatching is evidenced through data recorded over a temperaturerange of 5–50 K (Fig. 3a). The strong increase of emission at resonancefor both X and XX is the signature of the Purcell effect and enhancedemission into the modes. Autocorrelation measurements allow

extraction of a radiative lifetime of around 200–300 ps for each line,corresponding to the expected Fp 5 3–5.

In order to probe the two-photon states, the polarization-resolvedsecond order correlation function g2

X,XX(t) is measured under pulsednon-resonant excitation. Figure 3b shows two such coincidencecounts, with X measured in right circular polarization (R) and XXmeasured in right or left (L) circular polarization. The strong bunch-ing observed for the g2

X(R),XX(L)(t) correlation function shows thehigh probability that an L-polarized XX is followed by a R-polarizedX. Figure 3c shows the zero delay correlation peak on an enlargedscale. The positive delay of the peak corresponds to the case wherean XX photon is detected before a X photon, as expected in a radiativecascade. Negative delays correspond to the opposite situation, whereemission of XX after X is due to recapture of two excitons into thequantum dot. Only positive delay coincidences are considered tocreate entangled photon pairs. We define the correlation polarizationC 5 jn// 2 nHj/jn// 1 nHj, with n// the number of coincidences nor-malized to the two-photon flux for a co-polarized measurement basis,and nH the normalized number for a cross-polarized measurementbases. C is presented in Fig. 3d for consecutive histogram bins (width500 ps) within the zero delay peak presented in Fig. 3c. The correlationpolarization in the circular basis exceeds 60% for bins 0 and 1, anddecreases strongly towards negative delays, owing to recapture pro-cesses. Supplementary Fig. 2 shows that C is mostly independent of theexcitation power in the three polarization bases defined in Fig. 3legend. C deduced from integrated positive delay coincidences (bins0–4) is respectively 45%, 52% and 61% for the three measurementbases HXHXX/HXVXX, DXDXX/DXD9XX and RXLXX/RXRXX.

The entanglement of the two-photon state is quantified by perform-ing a quantum tomography measurement and by deriving the two-photon density matrix23 presented in Fig. 4a for positive delays. Mostcommon entanglement witnesses are satisfied (the Peres criterion23,24,

a H polarization1,344.3

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0.1

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–0.3 0.3 –0.3 0.3kx/k

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Figure 2 | Polarization properties of modes of the photonic molecule.a, Energy of the optical modes of the molecule for D 5 3.5mm and variousdistance CC9 measured on a calibration sample with Q 5 60,000 to allow highspectral resolution. Both M1 and M2 show polarization splitting smaller than60meV. The polarization splitting of mode M3 is also smaller than 70meV(not shown). The sources are fabricated with a moderate-quality-factorsample corresponding to a linewidth of 300–400meV (indicated as the grey-shaded region). b, Measurement of the radiation pattern for the modes M1,M2 and M3 of photonic molecule A (D 5 2.4mm, CC9 5 1.8mm) for twolinear polarizations: H and V, respectively parallel and perpendicular to themolecule axis, x. k is the amplitude of k as defined in Fig. 1.

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Figure 3 | Photon correlation measurements on molecule B. a, Emissionintensity (linear colour scale, arbitrary units) as a function of energy andtemperature. b, Measured second order correlation function, g2

X,XX. Theblack curve has been horizontally shifted for clarity. c, Zoomed-in view of thezero delay correlation peak in b. d, Correlation polarization C deduced fromthe data presented in c. The polarization detection settings are indicated asthe first letter for the X line and the second letter for the XX line. R and Lrefer to the right- and left-handed circular basis, respectively; H and V to thelinear basis parallel and perpendicular to the molecule axis, x, respectively;and D and D9 to the two linear diagonal polarizations. Molecule B hasD 5 2.4 mm, CC9 5 1.9 mm.

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concurrence25 and negativity26—see Table 1). The two-photon statepresents a fidelity of 67% to the (jHHæ 1 ei0.17pjVVæ)/!2 state when nophotons are discarded. This high degree of entanglement, among thebest reported for quantum-dot-based systems8–11, demonstrates thesuccessful implementation of the Purcell effect for the X line.Indeed, the corresponding X state presents S of around 1.5–3meV,which causes a phase shift w 5 StX/h between the jHHæ and jVVæcomponents of the two-photon state; w is proportional to the delayof X recombination, tX (ref. 27). This phase shift is evidenced whenextracting the density matrices calculated when taking into accountbin 0 counts only or bin 1 counts only: a phase shift of w < 0.34p takesplace in less than 500 ps (Table 1). To maintain a high fidelity to theY1 5 (jHHæ 1 jVVæ)/!2 Bell state, time gating has been previouslyapplied to discard X photons emitted at long delays. Obtaining aY1 fidelity of more than 67% for S 5 2.5meV without any Purcell effectwould necessitate a time gating of less than 200 ps, discarding morethan 90% of the emitted photons and strongly lowering the brightnessof the source27. By using the Purcell effect, and hence shortening thelifetime of the X transition, 73% of the photons are emitted in the first500 ps and exhibit a 68% fidelity to the Y1 state. Careful examinationof Fig. 3d shows that because of the limited temporal resolution of our

photodiodes (350 ps), negative delay events coming from recaptureprocesses partly contribute to bin 0 coincidences. The fidelity of oursource is therefore slightly limited by recapture processes. The use ofquasi-resonant excitation should lead to even higher fidelities bystrongly suppressing recapture processes.

The high brightness of our source first manifests itself by a eighttimes increase of intensity for both X and XX lines in resonance withthe molecule modes as compared to the planar cavity (SupplementaryFig. 3). The quantitative estimation of the brightness of our source isexplained in Methods. Figure 4b presents the average photon numberper pulse for X and XX as a function of excitation power. For a highexcitation power, an average of 0.35 X photons (0.5 XX photons)per pulse are collected in the first lens within a numerical apertureof 0.4 (Fig. 2b). Correcting these values to account for recaptureprocesses, this corresponds to an extraction/collection efficiency ofg 5 34% for each photon of the pair. This efficiency is consistent witha Purcell factor of around Fp 5 3–5 for each line, considering the equalreflectivity of the planar cavity mirrors, the molecule quality factor(Q 5 3,500) and the planar cavity quality factor (Q0 5 4,000)17.Figure 4b presents the rate of collected entangled photon pairs r foran excitation rate of rP 5 82 MHz; here r and rP are related byr 5 rPg2[1 2 g2

X,X(0)]1/2[1 2 g2XX,XX(0)]1/2, where the two last terms

are included to account for multiple photon emission due to recap-ture17. A rate of photon pairs collected in the first lens of r < 10 MHz isachieved.

To our knowledge, the present source of entangled photon pairs isbrighter than any existing source—in terms of photon pair rate perexcitation pulse collected in the first lens. By increasing the extractionefficiency by one order of magnitude for each photon of the pair, wehave increased by two orders of magnitude the brightness of thesource as compared to systems based on bare quantum dots. Thetime for measuring a cross-correlation is reduced to a few tens ofseconds as compared to typically several hours in previous reports.The extraction/collection efficiency of our source is now similar tothat obtained in parametric down-conversion systems. Because theprobability of creating a photon pair for each excitation pulse is 1 ascompared to 0.05 for parametric down-conversion systems, oursource is more than one order of magnitude brighter. To make thedegree of entanglement of our source closer to that demonstratedwith parametric down-conversion systems, better optimizing ofquantum dot annealing22 or electrical control of S (ref. 28) shouldbe used, as well as increased Purcell factors15,16. In a second step,resonant excitation could also be used to generate indistinguishablephotons29 and achieve entanglement distillation30.

With an optimized design of the cavity (unbalanced Bragg mirrorreflectivity) and a slightly better quality factor, the extraction effi-ciency would be as large as 80–90%. In this case, the present sourcewould be the brightest possible, with a photon rate only limited by theexcitation rate. As the whole radiative cascade takes place in less than0.5 ns thanks to the Purcell effect, we anticipate that an electricallypumped diode emitting polarization entangled photon pairs, with an80% overall efficiency and a 800 MHz photon rate, could be fabri-cated using a quantum dot coupled to a photonic molecule.

METHODS SUMMARYDevice fabrication. Two GaAs/Al0.9Ga0.1As microcavities embedding self-

assembled InAs quantum dots are used. One cavity (Q 5 60,000) is used to investi-

gate the molecule modes. The other (Q 5 4,000) is thermally annealed (867 uC for

30 s) to reduce S to 1–4meV. Afterwards, the planar cavity is spin-coated with a

positive photoresist and brought at 10 K. A 750-nm laser beam excites the

quantum dot emission without exposing the resist. Micro-photoluminescence

scanning allows centring on the quantum dot position with 50-nm accuracy. A

532-nm laser beam, superimposed on the red one, exposes the resist and defines a

disk centred on the quantum dot. The sample is moved by a distance CC9 and a

second disk is exposed. The exposure time is adjusted to obtain the desired pillar

diameter, D. The exposed disks serve as masks for pillar etching14.

Photon correlation measurements—data treatment. The 16 measurements

described in ref. 23 are performed to derive the density matrix. The sample is excited

Re( ) |Im( )|

T = 5 K

T = 5 K

0.4

0.3

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HHHV

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ulse 0.1

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1

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lect

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hoto

np

air

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(MH

z)

HV

HVVH

VH VV

X

10 100 10Excitation power (nW)

100

XX

VV

a

b

Figure 4 | Characterization of the source: entanglement and brightness.a, Density matrix of the two-photon state measured on molecule B forpositive delays for an excitation power of 130 nW. For simplicity, theabsolute value of the imaginary part is plotted, the sign of the imaginary partmatrix elements is indicated in the table (inset, right). b, Left: number of Xand XX collected photons for each excitation pulse as a function of theexcitation power. Right: collected entangled photon pair rate (MHz) as afunction of the excitation power.

Table 1 | Entanglement tests

Parameter All Delay.0 Bin 0 Bin1

Intensity fraction(delay . 0)

100% 73% 22%

Peres*, 0 20.12 20.16 20.20 20.3Negativity . 0 0.258 0.33 0.39 0.6Concurrence . 0 0.267 0.343 0.373 0.387

Fidelity to

( | HH. 1 | VV.)/!2

0.59 0.62 0.68 0.46

Largest eigenvalue 0.63 0.67 0.7 0.76

Eigenstate:

( | HH. 1 eiw | VV.)/!2

w 5 0.15p w 5 0.17p w 5 0.07p w 5 0.41p

Table summarizing the various parameters characterizing the entanglement of the two-photonstate deduced from the density matrix when taking into account all zero delay peak counts(column 2), positive delay counts only (column 3), bin 0 counts only (column 4) or bin 1 countsonly (column 5). w, phase shift resulting from the anisotropic exchange splitting, S (see maintext).* Peres criterion: see main text.

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using a 850-nm laser (5-ps pulses, 82 MHz). The emission is collected through a0.55 NA microscope objective and distributed in two arms of a Hanbury-Brown

and Twiss correlation set-up using a non-polarizing beam splitter. A set of linear

polarizers, half-wave and quarter-wave plates allows for polarization selection on

each arm. The signal is sent to spectrometers set to X or XX transition energies and

detected with avalanche photodiodes. (5–10) 3 105 counts s21 are measured at

saturation. No background subtraction is performed to derive the matrix.

Extraction efficiency measurements. To measure the source brightness, the laserbeam reflected by the planar bulk GaAs sample surface is measured under the

same conditions as the quantum dot emission. The response of the whole set-up is

measured to obtain a correspondence between a power measured in nanowatts

and a photodiode signal.

Received 6 February; accepted 26 April 2010.

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Supplementary Information is linked to the online version of the paper atwww.nature.com/nature.

Acknowledgements This work was partly supported by the European ProjectNanoEPR and by the French ANR P3N DELIGHT. We acknowledge A. Calvar andM. Larque for help with experiments, N. Dupuis for help with molecule modellingtheory and I. Robert-Philip for discussions. A.B. acknowledges discussions withB. Kraus and S. Iblisdir.

Author Contributions A.D. and P.S. were involved in all steps of this work. J.S. ranquantum dot anisotropic exchange splitting measurements and participated inphoton correlation measurements. A.B., O.K. and P.V. helped with the correlationexperimental set-up and participated in data analysis. P.V. also participated in thetheoretical study of photonic molecules. A.L. grew the samples. I.S. etched themicropillars and J.B. implemented the radiation pattern measurements. All authorsparticipated in scientific discussions and manuscript preparation.

Author Information Reprints and permissions information is available atwww.nature.com/reprints. The authors declare no competing financial interests.Readers are welcome to comment on the online version of this article atwww.nature.com/nature. Correspondence and requests for materials should beaddressed to P.S. (Pascale.Senellart@lpn.cnrs.fr).

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