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LETTERS

Ultrabright source of entangled photon pairs

Adrien Dousse1, Jan Suffczyn ´ski1{, Alexios Beveratos1, Olivier Krebs1, Aristide Lemaı ˆtre1, Isabelle Sagnes1,

Jacqueline Bloch1, Paul Voisin1& Pascale Senellart1

A sourceoftriggeredentangledphotonpairsisakeycomponentin

quantuminformationscience1;itisneededtoimplementfunctions

suchaslinearquantumcomputation2,entanglementswapping3and

quantum teleportation4. Generation of polarization entangled

photon pairs can be obtained through parametric conversion in

nonlinear optical media5–7or by making use of the radiative decay

of two electron–hole pairs trapped in a semiconductor quantum

dot8–11. Today, these sources operate at a very low rate, below 0.01

photonpairsperexcitationpulse,whichstronglylimitstheirappli-

cations. For systems based on parametric conversion, this low rate

is intrinsically due to the Poissonian statistics of the source12.

Conversely, a quantum dot can emit a single pair of entangled

photons with a probability near unity but suffers from a naturally

verylowextractionefficiency.Hereweshowthatthisdrawbackcan

beovercomebycouplinganopticalcavityintheformofa‘photonic

molecule’13toasinglequantumdot.Twocoupledidenticalpillars—

the photonic molecule—were etched in a semiconductor planar

microcavity, using an optical lithography method14that ensures a

deterministiccouplingtothebiexcitonandexcitonenergystatesof

a pre-selected quantum dot. The Purcell effect ensures that most

entangled photon pairs are emitted into two cavity modes, while

improving the indistinguishability of the two optical recombina-

tionpaths15,16.Apolarizationentangledphotonpairrateof0.12per

excitationpulse (with a concurrenceof0.34) iscollectedinthe first

lens.Ourresultsopenthewaytowardsthefabricationofsolidstate

triggered sources of entangled photon pairs, with an overall (cre-

ation and collection) efficiency of 80%.

Todate,mostquantuminformationandcommunicationprotocols

necessitatingentangledphotonpairshavebeenrealizedusingsources

based on parametric down-conversion2–7. These sources present

Poissonianstatistics:theprobabilitythateachpulsecontainstwopairs

ishalfthesquaredprobabilityofcontainingonlyone.Asthefidelityof

the protocol is degraded with increasing two-pair probability12, the

average photon pair per pulse has to be typically limited to 0.05.

Recently, it has been shown that a single semiconductor quantum

dot can emit polarization entangled photon pairs8–11. Two electron–

holepairs(abiexciton,calledheretheXXstate)trappedinaquantum

dot recombine radiatively through a two-photon cascade. As shown

schematically in Fig. 1a, two radiative recombination paths are pos-

sible through twoexciton (X) states of orthogonal polarization.If the

twoXstatesaredegenerate(anisotropicexchangesplittingS50),the

tworecombinationpathsareindistinguishableandthepairofemitted

photons is polarization entangled17. For excitation powers saturating

the XX transition, we can ensure that one photon pair is emitted for

each excitation pulse. However, in bulk material, less than 2% of the

pairscanbecollectedastheyareemittedisotropicallyinahighrefrac-

tive index material.

Tocollecttheemittedphotons,thequantumdotspontaneousemis-

sion can be controlled and funnelled into an optical cavity mode18.

When a quantum dot is spatially and spectrally coupled to a cavity

mode,itsemissionrateintothemodeisincreasedbythePurcellfactor

Fp,andafractionFp/(Fp11)ofthequantumdotemissionisfunnelled

intothemode.Singlephotonsourceswithanoverallefficiencyaround

38% have been realized following this scheme19. However, imple-

mentation of the same concepts to extract polarization entangled

photonpairsisnotstraightforward.First,XandXXphotonsareemit-

tedwithanenergydifferencethatusuallystronglyexceedsthewidthof

a single cavity resonance. Moreover, the coupling to the optical mode

must be independent of the polarization for both emitted photons, as

an increased Purcell factor for one recombination path would lead to

the generation of non-maximally entangled states. Finally, the radi-

ationpatternoftheopticalmodesshould notdependonpolarization,

in order to ensure that no ‘which-path’ information can be obtained

through the knowledge of the photon emission angle20.

In the present work, we fabricate an ultrabright source of entangled

photonpairsbydeterministicallycouplingaquantumdottoaphotonic

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

Hoz.a Street, 00-681 Warsaw, Poland.

Energy

Energy (meV)

M4–5

M3

M2

D

M1

D = 3 μm

1,350

Centre to centre distance,

CC′ (μm)

CC′

QD

3.63.42.82.4

z

y

k

x

1,348

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 for

nomenclature. b, Diagram of the source: two identical pillar microcavities

withdiameterDarecoupled.ThecentretocentredistanceislabelledCC9.A

single quantum dot (QD) is inserted in one of the pillars. k is the photon

wave vector. c, Energy of the optical mode of the photonic molecule for

D53mm and various centre to centre distances. The molecule modes are

labelled M1–M5. Dashed lines are guides to the eye.

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molecule.ToobtaintwocavityresonancesforbothXXandXphotons,

thequantumdotisinsertedinamicropillarcavitycoupledtoasecond

identical but empty micropillar (Fig. 1b). The mode energies of these

photonic molecules are presented in Fig. 1c, for an individual pillar

diameter D53mm and a set of centre-to-centre distances, CC9.

Reducing the distance CC9 leads to a coupling of the individual pillar

modes, resulting in a splitting of each mode. By choosing pillar dia-

meterDanddistanceCC9,itisthereforepossibletoindependentlytune

theenergiesofthephotonicmoleculemodes(M1–M5)andtheenergy

differences between them to match both X and XX energies. Figure 2

shows that, despite the reduction of symmetry, the properties of the

molecule’soptical modes areindependent of their polarizations over a

largerangeofparameters.Eachmode(M1–M5)ofthephotonicmole-

cule presents a polarization splitting of only few tens of microelectron

volts(Fig.2a).Tomeasuresuchsmallpolarizationsplittings,molecules

have been fabricated on a high-quality-factor (Q560,000) calibration

sample.Foramicrocavityofmoderatequalityfactor(Q54,500,mode

linewidtharound300meV),thissmallsplittingensuresastrongspectral

overlap of the modes both in H (horizontal) and V (vertical) polariza-

tions, needed to achieve a polarization independent Purcell effect.

Similarly,Fig.2bshowsradiationpatternsmeasuredonphotonicmole-

culeAwithD52.4mmandCC951.8mm:theradiationpatternsofthe

modesM1–M3 are identical inH and V polarization (overlap .98%).

Photonic molecules deterministically coupled to a single quantum

dotarefabricatedusinglowtemperatureinsituphotolithography21on

a planar microcavity in which a quantum dot layer is embedded, as

described in ref. 14. Two disks are exposed in the resist to define the

photonicmolecule,withthequantumdotlocatedatthecentreofone

pillar.Toemitpolarizationentangledphotons,Smustbesmallerthan

the X homogeneous linewidth17. Annealing22the sample reduced S to

1–4meV. Several molecules operating as sources of entangled photon

pairs between 5K and 52K were fabricated in one process. We report

theemissionpropertiesofmoleculeB,forwhichtheXlineisresonant

to mode 3, and the XX line is resonant to mode 2 at 5K. Thisspectral

matching is evidenced through data recorded over a temperature

rangeof5–50K(Fig.3a).Thestrongincreaseofemissionatresonance

for both X and XX is the signature of the Purcell effect and enhanced

emission into the modes. Autocorrelation measurements allow

extraction of a radiative lifetime of around 200–300ps for each line,

corresponding to the expected Fp53–5.

In order to probe the two-photon states, the polarization-resolved

secondordercorrelationfunctiong2X,XX(t)ismeasuredunderpulsed

non-resonant excitation. Figure 3b shows two such coincidence

counts, with X measured in right circular polarization (R) and XX

measured in right or left (L) circular polarization. The strong bunch-

ing observed for the g2X(R),XX(L)(t) correlation function shows the

high probability that an L-polarized XX is followed by a R-polarized

X. Figure 3c shows the zero delay correlation peak on an enlarged

scale. The positive delay of the peak corresponds to the case where

anXXphotonisdetectedbeforeaXphoton,asexpectedinaradiative

cascade. Negative delays correspond to the opposite situation, where

emission of XX after X is due to recapture of two excitons into the

quantum dot. Only positive delay coincidences are considered to

createentangled photon pairs.We definethecorrelation polarization

C5jn//2nHj/jn//1nHj, with n//the number of coincidences nor-

malizedtothetwo-photonfluxforaco-polarizedmeasurementbasis,

and nHthe normalized number for a cross-polarized measurement

bases. C is presented in Fig. 3d for consecutive histogram bins (width

500ps)withinthezerodelaypeakpresentedinFig.3c.Thecorrelation

polarization in the circular basis exceeds 60% for bins 0 and 1, and

decreases strongly towards negative delays, owing to recapture pro-

cesses.SupplementaryFig.2showsthatCismostlyindependentofthe

excitation power in the three polarization bases defined in Fig. 3

legend. C deduced from integrated positive delay coincidences (bins

0–4) is respectively 45%, 52% and 61% for the three measurement

bases HXHXX/HXVXX, DXDXX/DXD9XXand RXLXX/RXRXX.

Theentanglementofthetwo-photonstateisquantifiedbyperform-

ing a quantum tomography measurement and by deriving the two-

photon density matrix23presented in Fig. 4a for positive delays. Most

common entanglement witnesses are satisfied (the Peres criterion23,24,

a

H polarization

1,344.3

M3

M1

M2

Energy (meV)1,344.0

M2

1,343.7

1,343.4

2.5

CC′ (μm)

3.0

D = 3.5 μm

Polarization

V

H

M1

V polarization

0.3

0.1

–0.1

–0.3

0.3

0.1

–0.1

–0.3

ky/k

0.3

0.1

–0.1

–0.3

–0.30.3 –0.3

kx/k

0.3

b

Figure 2 | Polarization properties of modes of the photonic molecule.

a, Energy of the optical modes of the molecule for D53.5mm and various

distanceCC9measuredonacalibrationsamplewithQ560,000toallowhigh

spectralresolution.BothM1andM2showpolarizationsplittingsmallerthan

60meV. The polarization splitting of mode M3 is also smaller than 70meV

(not shown). The sources are fabricated with a moderate-quality-factor

sample 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 (D52.4mm, CC951.8mm) for two

linear polarizations: H and V, respectively parallel and perpendicular to the

molecule axis, x. k is the amplitude of k as defined in Fig. 1.

Energy (meV)

1,347.5

Coincidences

1,351

RL

M3

X

XX

M2

RL

X

Bin 0

–2–1

Time delay (ns)

001

Time delay (ns)

1

CRL/RR

Bin 1

XXX

Zero delay coincidences

XX

RR

RR

0

0

1

55

–2

Repetition period (×12 ns)

–222

12

–1

0.8

0.6

0.4

0.2

0.0

–10

Correlation polarization

Temperature (K)

T = 5 K

ba

dc

Figure 3 | Photon correlation measurements on molecule B. a, Emission

intensity (linear colour scale, arbitrary units) as a function of energy and

temperature. b, Measured second order correlation function, g2X,XX. The

blackcurvehasbeenhorizontallyshiftedforclarity.c,Zoomed-inviewofthe

zerodelaycorrelationpeakin b. d,CorrelationpolarizationCdeducedfrom

the data presented in c. The polarization detection settings are indicated as

the first letter for the X line and the second letter for the XX line. R and L

refertotheright-andleft-handedcircularbasis,respectively;HandVtothe

linear basis parallel and perpendicular to the molecule axis, x, respectively;

and D and D9 to the two linear diagonal polarizations. Molecule B has

D52.4mm, CC951.9mm.

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Page 3

concurrence25and negativity26—see Table 1). The two-photon state

presentsafidelityof67%tothe(jHHæ1ei0.17pjVVæ)/!2statewhenno

photons are discarded. This high degree of entanglement, among the

best reported for quantum-dot-based systems8–11, demonstrates the

successful 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 w5StX/h between the jHHæ and jVVæ

components of the two-photon state; w is proportional to the delay

of X recombination, tX(ref. 27). This phase shift is evidenced when

extracting the density matrices calculated when taking into account

bin0countsonlyorbin1countsonly:aphaseshiftofw<0.34ptakes

place in less than 500ps (Table 1). To maintain a high fidelity to the

Y15(jHHæ1jVVæ)/!2 Bell state, time gating has been previously

applied to discard X photons emitted at long delays. Obtaining a

Y1fidelityofmorethan67%forS52.5meVwithoutanyPurcelleffect

would necessitate a time gating of less than 200ps, discarding more

than90% of the emitted photonsand stronglyloweringthebrightness

of the source27. By using the Purcell effect, and hence shortening the

lifetime of theX transition,73% ofthephotonsare emitted in thefirst

500ps and exhibit a 68% fidelity to the Y1state. Careful examination

ofFig.3d shows that becauseof thelimitedtemporalresolutionofour

photodiodes (350ps), negative delay events coming from recapture

processes partly contribute to bin 0 coincidences. The fidelity of our

source is therefore slightly limited by recapture processes. The use of

quasi-resonant excitation should lead to even higher fidelities by

strongly suppressing recapture processes.

The high brightness of our source first manifests itself by a eight

times increase of intensity for both X and XX lines in resonance with

themoleculemodesascomparedtotheplanarcavity(Supplementary

Fig. 3). The quantitative estimation of the brightness of our source is

explainedinMethods.Figure4bpresentstheaveragephotonnumber

per pulse for X and XX as a function of excitation power. For a high

excitation power, an average of 0.35 X photons (0.5 XX photons)

per pulse are collected in the first lens within a numerical aperture

of 0.4 (Fig. 2b). Correcting these values to account for recapture

processes, this corresponds to an extraction/collection efficiency of

g534%foreachphotonofthepair.Thisefficiencyisconsistentwith

aPurcellfactorofaroundFp53–5foreachline,consideringtheequal

reflectivity of the planar cavity mirrors, the molecule quality factor

(Q53,500) and the planar cavity quality factor (Q054,000)17.

Figure 4b presents the rate of collected entangled photon pairs r for

an excitation rate of rP582MHz; here r and rPare related by

r5rPg2[12g2X,X(0)]1/2[12g2XX,XX(0)]1/2, where the two last terms

are included to account for multiple photon emission due to recap-

ture17.Arateofphotonpairscollectedinthefirstlensofr<10MHzis

achieved.

To our knowledge, the present source of entangled photon pairs is

brighter than any existing source—in terms of photon pair rate per

excitationpulsecollectedinthefirstlens.Byincreasingtheextraction

efficiency by one order of magnitude for each photon of the pair, we

have increased by two orders of magnitude the brightness of the

source as compared to systems based on bare quantum dots. The

time for measuring a cross-correlation is reduced to a few tens of

seconds as compared to typically several hours in previous reports.

The extraction/collection efficiency of our source is now similar to

that obtained in parametric down-conversion systems. Because the

probability of creating a photon pair for each excitation pulse is 1 as

compared to 0.05 for parametric down-conversion systems, our

source is more than one order of magnitude brighter. To make the

degree of entanglement of our source closer to that demonstrated

with parametric down-conversion systems, better optimizing of

quantum dot annealing22or electrical control of S (ref. 28) should

be used, as well as increased Purcell factors15,16. In a second step,

resonant excitation could also be used to generate indistinguishable

photons29and achieve entanglement distillation30.

With an optimized design of the cavity (unbalanced Bragg mirror

reflectivity) and a slightly better quality factor, the extraction effi-

ciency would be as large as 80–90%. In this case, the present source

wouldbethebrightestpossible,withaphotonrateonlylimitedbythe

excitation rate. As the whole radiative cascade takes place inless than

0.5ns thanks to the Purcell effect, we anticipate that an electrically

pumpeddiodeemittingpolarizationentangledphotonpairs,withan

80% overall efficiency and a 800MHz photon rate, could be fabri-

cated using a quantum dot coupled to a photonic molecule.

METHODS SUMMARY

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

assembledInAsquantumdotsareused.Onecavity(Q560,000)isusedtoinvesti-

gatethemoleculemodes.Theother(Q54,000)isthermallyannealed(867uCfor

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

positive photoresist and brought at 10K. 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 laserbeam, superimposedonthe red one, exposes the resistand definesa

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

describedinref.23areperformedtoderivethedensitymatrix.Thesampleisexcited

Re( )|Im( )|

T = 5 K

T = 5 K

0.4

0.3

0.2

0.1

HH

HV

VH

VV

HH

HV

VH

HH

HH

HV

HV

VH

VH

VV

VV

0

+

–

–

–

0

+

+

+

–

0

+

+

–

–

0

VV

0.4

0.3

0.2

0.1

HH

HV

VH

VV

HH

Collected photons

per pulse

0.1

10

1

0.1

0.01

0.01

Collected photon

pair rate (MHz)

HV

VH

X

XX

1010010

Excitation power (nW)

100

VV

a

b

Figure 4 | Characterization of the source: entanglement and brightness.

a, Density matrix of the two-photon state measured on molecule B for

positive delays for an excitation power of 130nW. For simplicity, the

absolutevalueoftheimaginarypartisplotted,thesignoftheimaginarypart

matrix elements is indicated in the table (inset, right). b, Left: number of X

and XX collected photons for each excitation pulse as a function of the

excitation power. Right: collected entangled photon pair rate (MHz) as a

function of the excitation power.

Table 1 | Entanglement tests

Parameter AllDelay.0

Bin 0

Bin1

Intensity fraction

(delay.0)

Peres*,0

Negativity.0

Concurrence.0

Fidelity to

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

Largest eigenvalue

Eigenstate:

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

100%

73%

22%

20.12

0.258

0.267

0.59

20.16

0.33

0.343

0.62

20.20

0.39

0.373

0.68

20.3

0.6

0.387

0.46

0.63

w50.15p

0.67

w50.17p

0.7

w50.07p

0.76

w50.41p

Table summarizing the various parameters characterizing the entanglement of the two-photon

state deduced from the density matrix when taking into account all zero delay peak counts

(column 2), positive delaycounts only (column 3), bin 0 counts only (column 4) or bin 1 counts

only (column 5). w, phase shift resulting from the anisotropic exchange splitting, S (see main

text).

*Peres criterion: see main text.

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using a 850-nm laser (5-ps pulses, 82MHz). The emission is collected through a

0.55 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

eacharm.ThesignalissenttospectrometerssettoXorXXtransitionenergiesand

detected with avalanche photodiodes. (5–10)3105countss21are measured at

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

Extractionefficiencymeasurements.Tomeasurethesourcebrightness,thelaser

beam reflected by the planar bulk GaAs sample surface is measured under the

sameconditionsasthequantumdotemission.Theresponseofthewholeset-upis

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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Acknowledgements This work was partly supported by the European Project

NanoEPR and by the French ANR P3N DELIGHT. We acknowledge A. Calvar and

M. Larque ´ for help with experiments, N. Dupuis for help with molecule modelling

theory and I. Robert-Philip for discussions. A.B. acknowledges discussions with

B. Kraus and S. Iblisdir.

Author Contributions A.D. and P.S. were involved in all steps of this work. J.S. ran

quantum dot anisotropic exchange splitting measurements and participated in

photon correlation measurements. A.B., O.K. and P.V. helped with the correlation

experimental set-up and participated in data analysis. P.V. also participated in the

theoretical study of photonic molecules. A.L. grew the samples. I.S. etched the

micropillarsandJ.B.implementedtheradiationpatternmeasurements.Allauthors

participated in scientific discussions and manuscript preparation.

Author Information Reprints and permissions information is available at

www.nature.com/reprints. The authors declare no competing financial interests.

Readers are welcome to comment on the online version of this article at

www.nature.com/nature. Correspondence and requests for materials should be

addressed to P.S. (Pascale.Senellart@lpn.cnrs.fr).

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