# Fileset

[enangle_20130705_postaccept.pdf](https://mdr.nims.go.jp/filesets/b5080c47-fdb4-4f85-9305-ac280e9c5f46/download)

## Creator

[Takashi Kuroda](https://orcid.org/0000-0001-6445-7673), [Takaaki Mano](https://orcid.org/0000-0002-6955-260X), Neul Ha, Hideaki Nakajima, Hidekazu Kumano, Bernhard Urbaszek, Masafumi Jo, Marco Abbarchi, [Yoshiki Sakuma](https://orcid.org/0000-0001-6804-7217), Kazuaki Sakoda, Ikuo Suemune, Xavier Marie, Thierry Amand

## Rights

©2013 American Physical Society[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

## Other metadata

[Symmetric quantum dots as efficient sources of highly entangled photons: Violation of Bell's inequality without spectral and temporal filtering](https://mdr.nims.go.jp/datasets/f2f824a1-df2d-4253-abc0-2d1f493cdc78)

## Fulltext

Symmetric quantum dots as efficient sources of highly entangled photons: violation ofBell’s inequality without spectral and temporal filteringTakashi Kuroda,1, 2 Takaaki Mano,1 Neul Ha,1, 2 Hideaki Nakajima,1, 3Hidekazu Kumano,3 Bernhard Urbaszek,4 Masafumi Jo,1 Marco Abbarchi,1Yoshiki Sakuma,1 Kazuaki Sakoda,1 Ikuo Suemune,3 Xavier Marie,4 and Thierry Amand41National Institute for Materials Science, 1 Namiki, Tsukuba 305-0044, Japan2Graduate School of Engineering, Kyushu University, Japan3Research Institute for Electronic Science, Hokkaido University, Sapporo 001-0021, Japan4Université de Toulouse, INSA-CNRS-UPS, LPCNO,135 avenue de Rangueil, 31077 Toulouse, France(Dated: July 5, 2013)An ideal emitter of entangled photon pairs combines the perfect symmetry of an atom with theconvenient electrical trigger of light sources based on semiconductor quantum dots. Our sourceconsists of strain-free GaAs dots self-assembled on a triangular symmetric (111)A surface. Theemitted photons reveal a fidelity to the Bell state as high as 86 (±2) % without post-selection. Weshow a violation of Bell’s inequality by more than 5 times the standard deviation, a prerequisite totest a quantum cryptography channel for eavesdropping. Due to strict nonlocal nature the sourcecan be used for real quantum processing without any post processing. The remaining decoherencechannel of the photon source is ascribed to random charge and nuclear spin fluctuations in and nearthe dot.PACS numbers: 78.67.Hc, 03.67.Bg, 78.55.-mIntroduction.— Entanglement is an essential resourcefor the implementation of quantum information process-ing. In addition to the demonstration of quantum cor-relations, a more stringent criterion for the direct im-plementation of an entangled photon source in quantumprocessing is the violation of Bell’s inequality, initiallyproposed as a experimental verification for quantum non-locality [1, 2]. In the original quantum cryptographyscheme of Artur K. Ekert [3] Bell’s inequality is usedas a test of the safety (against eavesdropping) of the keydistribution, as experimentally verified for sources basedon parametric down-conversion [4, 5]. The use of a semi-conductor quantum dot as a triggered photon source wasinitially proposed in 2000 [6]. Despite the concept beingstraightforward and analogous to that of an atomic cas-cade employed in the first demonstration of the violationof Bell’s theorem [7, 8], experimental implementation re-mains challenging due to the inherent anisotropy of dots.Most investigated dot systems suffer from structuralasymmetry, which induces a fine structure splitting (FSS)of the optically active exciton states [9, 10]. This FSSmakes radiative transition paths distinguishable, andthus strongly degrades or even prohibits entanglement inthe emitted photons [11]. Sophisticated techniques havebeen developed to recover the optical isotropy of dots,eventually demonstrating entangled photon pair emis-sion [12–19]. Despite impressive progress, these post-production techniques suffer from two main drawbacks.First, the application of external parameters such asstrain and/or electric fields has to be fine-tuned specifi-cally for each fabricated dot. Second, the degree of en-tanglement remains low compared with those routinelyachieved with other non-deterministic sources. Impor-tantly, a violation of Bell’s inequality has only beenshown up to now selecting photons emitted during arestricted temporal window [20] or with a very specificwavelength [14].Here we take a different approach to create a perfectlysymmetric photon source using an alternative methodof dot self-assembly, namely droplet epitaxy on (111)Asubstrates [21–23]. The photon pairs emitted by oursource exhibit a high polarization entanglement fidelityof f = 0.86± 0.02. The nonlocal nature of the observedentanglement is quantified in additional measurements innon-orthogonal polarization bases. We show that Bell’sinequality is violated as S = 2.33± 0.06 > 2 in as grownsamples, without any need for the spectral or temporalpost-selection previously employed for InAs dots [14, 20].This allows to use our source in principle directly in theEkert scheme for quantum cryptography as the quantumchannel is secured directly against eavesdropping by thecompleteness of quantum mechanics [24].Samples and set up.— Symmetry breaking in conven-tional dots is related to the growth of a cubic semicon-ductor along the [100] crystal axis. Since a (100) sur-face has atomic C2v symmetry, structures grown on itinevitably suffer from elongation, which lifts the degen-eracy of the exciton state [25] (see Fig. 1(a)). In contrast,in dots grown along the [111] axis, where both (111)A and(111)B surfaces have C3v symmetry, any source of struc-tural asymmetry is eliminated [26, 27]. As a consequencethe exciton states remain degenerate. Unfortunately, thestandard dot growth in the Stranski-Krastanov mode isprohibited along [111]. This obstacle is overcome byusing patterned substrates [28, 29] or droplet epitaxy[21, 30]. In InGaAs dots on a patterned (111)B substrate,the suppression of the FSS and classical correlations [29]have been demonstrated.2(a) (b)(c)C2vωx ≠ ωyC3vωx = ωyFIG. 1. (color online). (a) Conventional dots are grown ona (100) surface that has C2v symmetry. The elongation of adot shape and other anisotropic properties induce the asym-metry of the wave function envelope. This causes the excitonstate to split into two orthogonally-polarized states with en-ergies of ωx and ωy. In contrast, for dots grown on a (111)surface that has C3v symmetry the exciton states remain de-generate. (b) Atomic force microscope analysis of the samplesurface. (c) PL spectrum of an isolated GaAs dot. See textfor nomenclature.We employ GaAs dots grown on a (111)A substrate bydroplet epitaxy [21, 22]. This technique allows dots to beembedded in a lattice-matched barrier material, whichensures the robustness of the suppression of the FSSagainst microscopic randomness. Also, as droplet epitaxyis not strain driven a large variety of dot-barrier materialcombinations can be grown. This allows in principle fortuning of the dot emission wavelength while maintainingclose to zero FSS due to the high dot symmetry. This isan important advantage compared to annealed InGaAsdots, which also exhibit close to zero fine structure split-ting but for a specific wavelength band [31].The details of dot growth are reported elsewhere[21]. We employed a standard molecular beam epitaxymachine. After growing an Al0.3Ga0.7As layer on thegallium-rich surface of a GaAs (111)A substrate, wesupplied a 0.043 monolayer of gallium that formed Gadroplets at 400 ◦C. Then we supplied As4 to crystallizethe droplets into GaAs dots at 200 ◦C, followed byannealing at 500 ◦C. Several microscope observationswhich include in vacuo scanning tunneling microscopyand atomic force microscopy revealed the formationof dots with a truncated cone shape whose averageradius and height were 16 nm and 1.4 nm, respectively.Figure 1(b) shows the atomic force microscope image ofan investigated dot, which exhibits no lateral elongation.This is in stark contrast to dots grown on (100) surfaces,which exhibit significant elongation along [1-10] [32, 33].The GaAs dots were capped with an Al0.3Ga0.7Asbarrier.As an excitation source we used a pulsed semiconduc-tor laser with a high repetition frequency of 200 MHz[34–37]. We simultaneously counted three photonFIG. 2. (color online). Coincidence histograms between theXX and X photons for different polarization combinations.The signal at positive times is counted for the detection of anXX photon followed by that of an X photon. The two-photonprojection settings (such as LR) are indicated by the firstletter for XX photons and the second letter for X photons.They are plotted with a time bin of 128 ps.channels [38], i.e., XX photons projected onto a givenpolarization state, X photons projected onto anotherpolarization state (such as |R〉) and its orthogonalcomplement (such as |L〉). The use of three detectorsenabled us to eliminate the influence of excitationfluctuations on coincidence visibility [39]. The numberof coincidence was analyzed with a time-to-digitalconverter. The typical integration time was 10 minutesfor each polarization condition. All the experimentswere performed at 9 K.Correlation measurements: entanglementfidelity.– Figure 1(c) shows the photoluminescence(PL) spectrum of an isolated dot. It consists offour main lines, which are identified as being fromthe high-energy side, neutral excitons (X), positivelycharged excitons (X+), neutral biexcitons (XX), andnegatively charged excitons (X−) [40]. For performingthe correlation measurements, we select as-grown dotswithout a detectable FSS from the sample. PolarizedPL was analyzed with a spectral resolution comparableto the radiative width, which is expected to be 1.2 µeV(560 ps in terms of lifetime; see Fig. 4(a)). Small butnon-zero FSS values are confirmed for most of thedots, and they are distributed around a mean valueof 10 ± 5 µeV. This is noticeably smaller than boththe typical values for Stranski-Krastanov grown dots,and those for droplet epitaxial GaAs dots grown on(100) [32]. In the investigated sample 5 % of the dotsshow no detectable FSS. We have measured the photoncorrelations in more than 10 selected dots and they allexhibit entanglement. Figure 2 shows the results ofphoton correlation measurements in a typical dot. See,Supplementary Fig. 1 [39] for spectral characterizationin this dot. L,R,H and V indicate projections along the3left-handed circular, right-handed circular, linear labora-tory horizontal, and vertical polarizations, respectively.D is linear diagonal with a polarization axis tilted by45◦ from H, and A is anti-diagonal where A ⊥ D. Thetop panel in Fig. 2(a) shows a coincidence histogramfor L-polarized XX photons and R-polarized X photons(denoted by LR). The presence of a central peakconfirms a radiative cascade. The XX and X photons areclearly correlated, resulting in a higher probability thanthat for detecting uncorrelated photons. The centralpeak disappears for a polarization combination of LL(second panel). Thus, the probability of observing bothXX and X photons in L is close to zero. The sameanti-correlation is confirmed for RR (third panel), but apositive correlation is recovered for RL (bottom panel).These results imply that the two-photon polarizationstate can be approximated by one of the Bell (maximallyentangled) states,|Ψ〉 =|LR〉+ |RL〉√2. (1)A key criterion for entanglement is the presence of acorrelation independent of the chosen polarization basis.Figure 2(b) shows coincidence histograms for rectilinearpolarizations. A positive correlation appears for parallelpolarizations (HH,V V ), while it disappears for perpen-dicular polarizations (HV, V H). These results agree withthe expression of the Bell state of Eq. 1 in a linear polar-ization basis,We define the correlation visibility C =∣∣(n‖ − n⊥)/(n‖ + n⊥)∣∣, where n‖ is the number ofcoincidences normalized with the two-photon flux for aco-polarized basis, and n⊥ is that for a cross-polarizedbasis (see, Supplementary information for the normal-ization procedure [39]). An ideal source is expected toshow C = 1 for any orthogonal basis set. Our resultsshow that C = 0.87± 0.03 for R/L and C = 0.78± 0.03(0.77 ± 0.03) for H/V (D/A). The visibility for linearpolarizations is found to be approximately independentof the polarization direction, which demonstrates theisotropic characteristic of our source (SupplementaryFig. 2(a)[39]). The higher C value for the circular basisthan for the linear bases originates from the hyperfineinteraction of the exciton with nuclear spins – see,Supplementary Material [39] and references . The entan-glement fidelity is defined as the projection amplitudeof a measured polarization state on a target Bell state,which is given by f = (1 +CR/L +CH/V +CD/A)/4 [20].Our results reveal that f = 0.86 (±0.02), which is muchlarger than the classical limit of 0.5, and rates among thebest reported in previous studies on dot based photonsources [12, 15–18].Experimental violation of Bell’s inequality.— En-tangled photon pair emission from QDs is an importantmilestone, but the most powerful applications of entan-glement are linked to nonlocality, which is only assuredby the violation of Bell’s inequality [1]. To verify this ex-(a)(b)RLHθDRe(ρ)|Im(ρ)|FIG. 3. (color online). (a) Normalized coincidence counts as afunction of the X polarization angle (θX) for four different val-ues of the XX polarization (θXX). The error bars include onlyPoissonian noise. The sinusoidal fits are also shown by lines.(b) Tomographic representation of the measured two-photonstate. The density matrix is reconstructed using coincidencecounts for 36 projection bases. The absolute values are plot-ted for the imaginary part of the matrix, and their signs areshown in the top of each element.perimentally, we have performed additional photon corre-lation experiments in non-orthogonal polarization bases.Figure 3(a) shows normalized coincidence counts as afunction of the polarization angle of X (θX) at four differ-ent angle settings for XX polarization (θXX). Note thatwe define the angle of θ as the polar angle of a polariza-tion state that moves in the RLHV plane of the Poincarésphere (θ = 0 for R and θ = 90◦ for H). It was exper-imentally controlled by the application of phase retar-dance to each beam using liquid crystals. The azimuth-angle dependence was also measured and shown in Sup-plementary Fig. 2(b) [39]. Sinusoidal oscillations in thecoincidence counts provide evidence of quantum inter-ference, distinct from classical correlation. The maxi-mum violation of Bell’s inequality in the Clauser-Horne-Shimony-Holt form [41] is expected to appear for polar-ization correlations with θXX = 0◦, 90◦, 180◦, 270◦ andθX = 45◦, 135◦, 225◦, and 315◦. We measure the coinci-dence counts for these settings, and estimate the S pa-rameter to be 2.33±0.06 > 2. It clearly violates Bell’s in-equality by more than five times the standard deviation,which is definite proof of the nonlocality of the measuredphotons. The importance of nonlocality of entanglementis seen in the Ekert protocol [3]. If an eavesdropper mea-sures either state of an entangled pair, it becomes localreality and nonlocality vanishes. This is why Bell’s in-equality can serve as a secure test against eavesdropping.Other applications such as quantum teleportation andentanglement swapping also rely on nonlocality. Conse-4FIG. 4. (color online). (a) The decay of circularly polarizedPL signals for the X line after short-pulsed and quasi-resonantexcitation. Here we study the same dot as that used in thecorrelation measurement. (b) The degree of circular polariza-tion, defined as (I(σ) − I(σ̄))/(I(σ) + I(σ̄)), where I(σ) andI(σ̄) are the co-circular and cross-circular intensities, respec-tively. The broken line is an exponential fit to data, with anestimated decay time of Γ−1S =1.5 ns. The inset shows theenergy diagram of the exciton state. In the experiment, weused a short-pulsed parametric oscillator that emitted 4 pspulses with a wavelength shifted by an optical phonon en-ergy of 37 meV from the X line. The excitation polarizationwas set as circular, and temporally modulated to maintain anequilibrium nuclear environment. Polarized PL was detectedby a fast-response photomultiplier tube with a response timeof 40 ps.quently, our device is the only QD source reported so far,which can be used for real applications without applyingtemporal or spectral filtering techniques.Figure 3(b) shows the reconstructed density matrix ofthe two-photon state using the correlation measurementresults of 36 projection sets (X,XX ∈ {R,L,H, V,D,A})with the aid of a maximum-likelihood technique [42]. Thepresence of four real values at the corner of the ma-trix, with negligible values for the others, demonstratesthe superior characteristics of our source. The matrixhas a partial transpose with the minimum eigenvalue of−0.36 < 0, which clearly satisfies the Peres criterion ofentanglement, which assures quantum inseparability [43].The density matrix allows us to evaluate the degree ofcoherence and the degree of mixedness of the measuredstate in terms of the tangle (T ) and the linear entropy(SL), respectively. From T we derive one of the most ba-sic measure of the entanglement of formation (EF ) [44].Our results reveal that (T, SL, EF ) = (0.53, 0.32, 0.63).These values are the best among those achieved by sim-ilar types of photon sources, even without the postselec-tion (or any local operation) of the photons.The small but apparent deviation in the measuredphotons from the ideal Bell pairs (Eq. 1) is due to thedepolarization of the exciton state. Figure 4(a) showsthe time-resolved PL of the X line after polarized quasi-resonant excitation. Note that we study the same dot asthat used in the correlation measurement. The PL decayshows a single exponent with a lifetime of Γ−11 = 560 ps,which is fully consistent with the exciton dipole momentdetermined by a Rabi oscillation measurement [45]. Fig-ure 4(b) shows the circular polarization degree, which de-cays with Γ−1s = 1.5 ns. The fact that Γs � Γ1 supportsthe view that polarization memory is well conserved untilrecombination. Nevertheless, a finite value for Γs givesrise to a finite probability of observing depolarized pho-tons. We can estimate the correlation visibility of photonpairs to be Γ1/(Γ1 + Γs) ≈ 0.7, which is in fairly goodagreement with the observed C value. These findings in-dicate that our source is neither affected by incoherentnoise associated with carrier recapturing [17, 20] nor lightemission from other luminescent centers than the dot.The degree of entanglement is thus purely limited by thescattering of excitons. We ascribe the exciton depolar-ization to random charge and nuclear spin fluctuationsin and near the dot. The slowly varying environmentrepresents a remaining source of asymmetry that limitsthe degree of quantum interference even in a solid-statephoton source based on symmetric dots, as discussed inthe supplementary material[39].In summary, we have demonstrated the generation ofentangled photon pairs using a strain-free GaAs dot asa symmetric artificial-atom cascade on (111)A surfaces.A clear violation of Bell’s inequality is observed in cor-relation measurements that do not rely on postselectionthrough filtering or tuning. Using our source in quantumcryptography applications, would allow safe key distribu-tion not based on a mathematical difficulty but on a fun-damental physical law that protects the system, namelythe completeness of quantum mechanics [3]. The purityof our source also paves the way for using droplet dotbased emitters to investigate the exact connection be-tween the security of quantum cryptography and tests ofquantum non-locality [24] in the solid state. We clari-fied the impact of the remaining exciton depolarizationon the degree of entanglement in the emitted pairs. Theinfluence of depolarization could be efficiently suppressedin the future using the Purcell enhancement of the radia-tive rate [17] or time-domain filtering with fast-responsedetectors [20]. As droplet epitaxy is not strain driven,a large variety of dot-barrier material combinations canbe grown. This opens up the possibility of extending thecurrent emission wavelengths around 700 nm (that yieldsthe highest photon counting efficiency in Si-based detec-tors) towards the wavelength regions suitable for long-distance fiber-based telecommunication. This work wassupported in part by a Grant-in-Aid from JSPS, ITNSpinOptronics and ERC StG OptoDNPcontrol (B.U.).Note added: After submission of this manuscript, en-tangled photon emission from dots grown on patterned(111)B substrates has been reported [46].5[1] J. S. Bell, Physics 1, 195 (1964).[2] A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47,777 (1935).[3] A. K. Ekert, Phys. Rev. Lett. 67, 661 (1991).[4] T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, andA. Zeilinger, Phys. Rev. Lett. 84, 4729 (2000).[5] D. S. Naik, C. G. Peterson, A. G. White, A. J. Berglund,and P. G. Kwiat, Phys. Rev. Lett. 84, 4733 (2000).[6] O. Benson, C. Santori, M. Pelton, and Y. Yamamoto,Phys. Rev. Lett. 84, 2513 (2000).[7] A. Aspect, P. Grangier, and G. Roger, Phys. Rev. Lett.47, 460 (1981).[8] A. Aspect, P. Grangier, and G. Roger, Phys. Rev. Lett.49, 91 (1982).[9] D. Gammon, E. S. Snow, B. V. Shanabrook, D. S. Katzer,and D. Park, Science 273, 87 (1996).[10] M. Bayer, A. Kuther, A. Forchel, A. Gorbunov, V. B.Timofeev, F. Schäfer, J. P. Reithmaier, T. L. Reinecke,and S. N. Walck, Phys. Rev. Lett. 82, 1748 (1999).[11] C. Santori, D. Fattal, M. Pelton, G. S. Solomon, andY. Yamamoto, Phys. Rev. B 66, 045308 (2002).[12] R. M. Stevenson, R. J. Young, P. Atkinson, K. Cooper,D. A. Ritchie, and A. J. Shields, Nature 439, 178 (2006).[13] R. J. Young, R. M. Stevenson, P. Atkinson, K. Cooper,D. A. Ritchie, and A. J. Shields, New J. Phys. 8, 29(2006).[14] N. Akopian, N. H. Lindner, E. Poem, Y. Berlatzky,J. Avron, D. Gershoni, B. D. Gerardot, and P. M.Petroff, Phys. Rev. Lett. 96, 130501 (2006).[15] R. Hafenbrak, S. M. Ulrich, P. Michler, L. Wang,A. Rastelli, and O. G. Schmidt, New J. Phys. 9, 315(2007).[16] A. Muller, W. Fang, J. Lawall, and G. S. Solomon, Phys.Rev. Lett. 103, 217402 (2009).[17] A. Dousse, J. Suffczyǹski, A. Beveratos, O. Krebs,A. Lemâıtre, I. Sagnes, J. Bloch, P. Voisin, and P. Senel-lart, Nature 466, 217 (2010).[18] M. Ghali, K. Ohtani, Y. Ohno, and H. Ohno, Nat. Com-mun. 3:661 (2012), 10.1038/ncomms1657.[19] R. Trotta, E. Zallo, C. Ortix, P. Atkinson, J. D. Plumhof,J. van den Brink, A. Rastelli, and O. G. Schmidt, Phys.Rev. Lett. 109, 147401 (2012).[20] R. J. Young, R. M. Stevenson, A. J. Hudson, C. A. Nicoll,D. A. Ritchie, and A. J. Shields, Phys. Rev. Lett. 102,030406 (2009).[21] T. Mano, M. Abbarchi, T. Kuroda, B. McSkimming,A. Ohtake, K. Mitsuishi, and K. Sakoda, Appl. Phys.Express 3, 065203 (2010).[22] G. Sallen, B. Urbaszek, M. M. Glazov, E. L. Ivchenko,T. Kuroda, T. Mano, S. Kunz, M. Abbarchi, K. Sakoda,D. Lagarde, A. Balocchi, X. Marie, and T. Amand, Phys.Rev. Lett. 107, 166604 (2011).[23] M. V. Durnev, M. M. Glazov, E. L. Ivchenko, M. Jo,T. Mano, T. Kuroda, K. Sakoda, S. Kunz, G. Sallen,L. Bouet, X. Marie, D. Lagarde, T. Amand, and B. Ur-baszek, Phys. Rev. B 87, 085315 (2013).[24] N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev.Mod. Phys. 74, 145 (2002).[25] R. Seguin, A. Schliwa, S. Rodt, K. Pötschke, U. W. Pohl,and D. Bimberg, Phys. Rev. Lett. 95, 257402 (2005).[26] R. Singh and G. Bester, Phys. Rev. Lett. 103, 063601(2009).[27] A. Schliwa, M. Winkelnkemper, A. Lochmann, E. Stock,and D. Bimberg, Phys. Rev. B 80, 161307 (2009).[28] Y. Sugiyama, Y. Sakuma, S. Muto, and N. Yokoyama,Appl. Phys. Lett. 67, 256 (1995).[29] A. Mohan, M. Felici, P. Gallo, B. Dwir, A. Rudra, J.Faist, and E. Kapon, Nature Photon. 4, 302 (2010) andNature Photon. Retraction 6, 793 (2012).[30] E. Stock, T. Warming, I. Ostapenko, S. Rodt, A. Schliwa,J. A. Töfflinger, A. Lochmann, A. I. Toropov, S. A.Moshchenko, D. V. Dmitriev, V. A. Haisler, and D. Bim-berg, Appl. Phys. Lett. 96, 093112 (2010).[31] R. J. Young, R. M. Stevenson, A. J. Shields, P. Atkin-son, K. Cooper, D. A. Ritchie, K. M. Groom, A. I. Tar-takovskii, and M. S. Skolnick, Phys. Rev. B 72, 113305(2005).[32] M. Abbarchi, C. A. Mastrandrea, T. Kuroda, T. Mano,K. Sakoda, N. Koguchi, S. Sanguinetti, A. Vinattieri,and M. Gurioli, Phys. Rev. B 78, 125321 (2008).[33] Y.-H. Liao, C.-C. Liao, C.-H. Ku, Y.-C. Chang, S.-J.Cheng, M. Jo, T. Kuroda, T. Mano, M. Abbarchi, andK. Sakoda, Phys. Rev. B 86, 115323 (2012).[34] The laser pulse width was 80 ps, the wavelength 640 nm.The high repetition pumping allowed us to measure thecorrelation profile with high visibility [35, 36]. In thiscondition, photocarriers were pumped to the barrier con-tinuum, and then relaxed to dots before recombination.Linear excitation polarization was employed to avoid theeffects of nuclear polarization [37].[35] G. Oohata, R. Shimizu, and K. Edamatsu, Phys. Rev.Lett. 98, 140503 (2007).[36] T. Kuroda, T. Belhadj, M. Abbarchi, C. Mastrandrea,M. Gurioli, T. Mano, N. Ikeda, Y. Sugimoto, K. Asakawa,N. Koguchi, K. Sakoda, B. Urbaszek, T. Amand, andX. Marie, Phys. Rev. B 79, 035330 (2009).[37] T. Belhadj, T. Kuroda, C.-M. Simon, T. Amand,T. Mano, K. Sakoda, N. Koguchi, X. Marie, and B. Ur-baszek, Phys. Rev. B 78, 205325 (2008).[38] The photoluminescence emission from a single dot wascollected by an objective lens with a numerical apertureof 0.75, and split into two beams with different spectralcomponents, one comprising the X line and the othercomprising the XX line with a bandwidth of 200 µeV.Each beam was coupled to a polarization analyzer anddetected by an avalanche photodiode. The typical countrate was 30,000 counts s−1 for X photons, and 6,000counts s−1 for XX photons, when the polarization an-alyzer was removed.[39] See Supplemental Material at [URL].[40] M. Abbarchi, T. Kuroda, T. Mano, K. Sakoda, C. A.Mastrandrea, A. Vinattieri, M. Gurioli, and T. Tsuchiya,Phys. Rev. B 82, 201301 (2010).[41] J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt,Phys. Rev. Lett. 23, 880 (1969).[42] D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G.White, Phys. Rev. A 64, 052312 (2001).[43] A. Peres, Phys. Rev. Lett. 77, 1413 (1996).[44] W. K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).[45] K. Kuroda, T. Kuroda, K. Watanabe, T. Mano,K. Sakoda, G. Kido, and N. Koguchi, Appl. Phys. Lett.90, 051909 (2007).6[46] G. Juska, V. Dimastrodonato, L. O. Mereni, A. Gocalin- ska, and E. Pelucchi, Nature Photon. DOI10.1038,NPHOTON.2013.128 (2013).