Single spin optical read-out in CdTe/ZnTe quantum dot studied by photon correlation spectroscopy
J. Suffczynski, K. Kowalik, T. Kazimierczuk, A. Trajnerowicz, M. Goryca, P. Kossacki, A. Golnik, M. Nawrocki, J. A. Gaj
aa r X i v : . [ c ond - m a t . o t h e r] M a y Single spin optical read-out in CdTe/ZnTe quantum dot studied by photon correlationspectroscopy
J. Suffczy´nski, ∗ K. Kowalik, T. Kazimierczuk, A. Trajnerowicz,M. Goryca, P. Kossacki, A. Golnik, M. Nawrocki, and J. A. Gaj
Institute of Experimental Physics, University of Warsaw, Ho˙za 69, 00-681 Warsaw, Poland
G. Karczewski
Institute of Physics, Polish Academy of Sciences, Al. Lotnik´ow 32/64, 02-668 Warsaw, Poland
Spin dynamics of a single electron and an exciton confined in CdTe/ZnTe quantum dot is investi-gated by polarization-resolved correlation spectroscopy. Spin memory effects extending over at leasta few tens of nanoseconds have been directly observed in magnetic field and described quantitativelyin terms of a simple rate equation model. We demonstrate an effective (68%) all-optical read-out ofthe single carrier spin state through probing the degree of circular polarization of exciton emissionafter capture of an oppositely charged carrier. The perturbation introduced by the pulsed opticalexcitation serving to study the spin dynamics has been found to be the main source of the polariza-tion loss in the read-out process. In the limit of low laser power the read-out efficiency extrapolatesto a value close to 100%. The measurements allowed us as well to determine neutral exciton spinrelaxation time ranging from 3 . ± . B = 0 T to 16 ± B = 5 T. PACS numbers: 78.55.Et, 73.21.La, 78.67.-n, 78.47.+p, 42.50.Dv
I. INTRODUCTION
One of the consequences of energy quantization insemiconductor quantum dots (QDs) is the suppression ofspin relaxation of confined carriers and excitons.
Re-cent experiments conducted on ensemble of III-V QDshave demonstrated that electrons confined in the QDspreserve their spin polarization over microsecond oreven millisecond timescales. It has been also shown, thatspin of the electron confined in the QD can be effec-tively optically read and written . These features,complementing the fact that individual QDs can be usedas non-classical light sources make QDs very attrac-tive for implementation in the developing field of quan-tum information, where polarization-encoded singlephotons would be utilized. However, several difficultiesneed to be overcome in order to achieve effective oper-ation of quantum qubits based on single QDs. One ofthem is native QD anisotropy, which does not influencethe spin state of a single electron, but determines theeigenfunctions of exciton and induces linear polarizationof its emission. Thus, even if the spin of the carrier iseffectively stored, it can not be effectively read . The po-larization of exciton which is formed in the optical read-out of the carrier spin state will be determined by theanisotropy. A lot of effort has been devoted to develop-ment of fabrication technique enabling creation of QDspossessing no anisotropy, however no straightforwardmethod has been established so far.In this work single carrier spin memory effects are stud-ied by correlation spectroscopy technique. Descriptionof the experimental results with a simple rate equationmodel allowed us to determine the degree of the carrierspin polarization conserved in the process of optical read-out . We quantify the impact of biexciton formation on the loss of the carrier polarization memory. We deter-mine also neutral exciton ( X ) spin relaxation time - serv-ing as a one of the model parameters.The paper is organized as follows. Section II providesinformation on the sample studied and the experimen-tal setup. Experimental results are collected in Sec. III,which is divided in three parts. A summary of stan-dard cw microphotoluminescence ( µ -PL) characteriza-tion of the sample (Sec. III A) is followed by results ofpolarized biexciton-exciton ( XX - X ) crosscorrelation mea-surements (Sec. III B), supplying information on X spinrelaxation time. Charged exciton-neutral exciton ( CX - X ) polarized crosscorrelation experiments reveal singlecarrier spin memory through effective optical read-out (Sec. III C). Section IV contains the rate equation modeldescription of the experimental data. II. SAMPLE AND EXPERIMENTAL SETUP
Detailed macro- and micro-PL characterization of thesample used in this work has been presented in Refs. 14,15,16. The sample contains a single layer of QDs, selfassembled out of two monolayers of CdTe, embeddedbetween ZnTe barriers. Typical density of the QDs is10 cm − . The sample was mounted directly on the front surfaceof a mirror type microscope objective (numerical aper-ture = 0.7, spatial resolution ∼ µ m) and cooled downto T = 1.7 K in a pumped helium cryostat with a su-perconducting coil. Microphotoluminescence was excitednon-resonantly (above the barrier band gap) with short( < :Al O laser pulses, delivered every 6.6 nsat wavelength of 400 nm (after frequency doubling). Theexcitation beam was linearly polarized.Photon correlations were measured in a Hanbury-Brown and Twiss (HBT) type setup with spectral fil-tering. PL signal arising from the sample was dividedin two beams on a polarizing beamsplitter (BS) and di-rected to the entrances of two grating monochromators(spectral resolution 200 µ eV). The monochromators weretuned to pass photons from a single excitonic transition,chosen independently on each spectrometer. The signalswere then detected by two avalanche photodiodes. Thediodes were connected to start and stop inputs of coin-cidence counting electronics producing histogram (4096time bins of 146 ps each) of correlated counts versus timeinterval separating photon detection on the first and onthe second diode. Total temporal resolution of the setupis estimated at 1.1 ns.Polarization optics (combinations of halfwave andquarterwave retarders with a linear polarizer) imple-mented in the HBT setup enabled detection of thesecond-order correlation function for four linear or fourcircular polarization combinations. III. EXPERIMENTAL RESULTSA. Sample characterization
The µ -PL from the QD layer covers the energy rangebetween 2.20 eV and 2.32 eV. Excitonic transitions stud-ied in this work were selected from the low energy tail(2.20 eV – 2.24 eV) of the µ -PL spectrum, since in thisregion lines of individual QDs are well resolved and back-ground counts are negligible. Polarization resolved µ -PL spectrum of the QD selected for this study taken at B = 0 T is presented in Fig. 1(a). Dependence of inte-grated line intensities on excitation power combined withauto- and crosscorrelation data allowed us to identify theobserved transitions as neutral exciton ( X ), charged ex-citon ( CX ) and biexciton ( XX ) recombination. As vis-ible in Fig. 1(a), X and XX lines exhibit anisotropic ex-change splitting (AES) in two linearly polarized compo-nents, resulting from electron-hole exchange interactionin an anisotropic QD. In order to determine the value of the AES and direc-tions of linear polarizations of the QD emission, energypositions of X , CX and XX as a function of detectionpolarization angle were measured (Fig. 2). No energyvariation occurs in the case of CX , in agreement with theexpectation (two identical carriers of the trion are in asinglet state). In the case of X and XX , oscillations oftransition energy are observed with opposite phase andthe same amplitude for both lines. For the QD discussedbelow AES was determined to be 182 ± µ eV.A common H-V basis of linear polarizations corre-sponding to QD symmetry axes was determined as ro-tated 58 ◦ ± ◦ from laboratory axes. The QD symmetryaxes do not correspond to the main crystallographic axesof the sample, in agreement with previous anisotropymeasurements revealing random anisotropy orientation Photon Energy (meV)
B = 5 T
XCX
V H (b) - P L I n t e n s it y ( a r b . un it s ) B = 0 T (a) XX FIG. 1: (Color online) Polarization resolved emission spectraof the selected quantum dot at B = 0 T (a) and B = 5 T(b) detected in linear H-V and circular σ +/ σ − polarizationbases respectively. Excitation at the energy of 3.1 eV withthe average power ∼ SAT (the saturation power of the Xemission P
SAT =1.2 µ W at B = 0 T). of CdTe/ZnTe QDs. Determination of the excitonic ef-fective Land´e factor based on Zeeman splitting measure-ments (Fig. 3) performed in magnetic field ranging up to5 T gave approximately the same value g = − . ± . B. Polarized XX - X crosscorrelation measurements In this section, we present time and polarization re-solved photon correlations involving biexciton - excitoncascade. The measurements were performed in magneticfield ranging up to 5 T and provided an estimate of the X spin relaxation time. The spin relaxation time was foundto increase with magnetic field.In the experiment, the monochromators were set to de-tect XX and X transition by the start and stop diode, re-spectively. The obtained correlation histograms suppliedinformation on relative polarizations of XX and X pho-tons emitted subsequently in XX radiative decay. Dueto the pulsed excitation, the histograms consist of peaksspaced equally by the repetition period of the excitationpulses (Fig. 4(a)). The XX - X crosscorrelation histogramsmeasured at B = 0 T in the linear H-V polarization basis E n e r gy ( m e V ) Rotation Angle (degree)
XXCX E n e r gy ( m e V ) (c)(b) X E n e r gy ( m e V ) (a) FIG. 2: (Color online) Emission energies of (a) X , (b) CX and(c) XX versus angle of detected linear polarization (points).Solid line represents a sinusoidal fit (a) and (c), or a linear fit(b). is shown in Fig. 4(a). The normalized areas of the centralpeak in Fig. 4(a) are 5 . ± . . ± . . ± .
02 and 0 . ± . − ◦ / + 45 ◦ polarization ba-sis has not revealed any polarization dependent effects onthe zero delay peak (not shown). Similarly, no polariza-tion effects were detected in the measurement performedin circular σ + /σ − basis (Fig. 4(b)). Thus, XX decayproduces a pair of classically correlated photons, whichis expected for a QD with a reduced symmetry. Degree of the correlation in linear H/V polariza-tion basis, estimated following Ref. 21, amounts to χ HV = 0.86 ± .
06. The nonzero probability of de-tecting perpendicularly polarized photon pairs originatesmostly from the relaxation of excitonic spin occurringover the exciton lifetime. Using the formula derived bySantori et al. (Ref. 21) and basing on the X lifetime( τ radX = 0 . ± .
05 ns) obtained from an independentexperiment performed on the same QD, we estimate X spin relaxation time at T X = 3 . ± . T X value is an order of magnitude larger thanthe excitonic radiative lifetime, in agreement with pre- XXCX E - E X ( B = ) ( m e V ) Magnetic field (T) X FIG. 3: (Color online) Energy of X , CX and XX emissionrelative to zero-field X energy, measured in both circular po-larizations as a function of magnetic field in Faraday config-uration. Solid lines represent the calculation of the Zeemansplitting with Land´e factor g = − . vious results obtained on InAs/GaAs , CdSe/ZnSe and CdTe/ZnTe QDs.Mixing of excitonic states with angular momentumM = ± As the Zeeman splitting becomes domi-nant, the linearly polarized excitonic doublet observed in µ -PL spectra converts in two lines with nearly perfectorthogonal circular polarizations (Fig. 1(b)) correspond-ing to almost pure M = ± provides an estimate of ellipticity of the eigen-states and of the resulting circular polarization degreeat 98.3% at B = 5 T. This Zeeman-controlled emissionis demonstrated in polarized crosscorrelations measuredat B = 5 T on spin split XX and X lines in the circu-lar basis (Fig. 4(c)). As seen in Fig. 4(c), XX - X photonpairs contributing to the central peak exhibit significant,positive (negative) correlation for opposite (equal) cir-cular polarizations, in contrast to the result obtained at B = 0 T (Fig. 4(b)). The respective normalized values ofthe central peaks in histograms of Fig. 4(c) provide thedegree of polarization correlation χ σ + σ − = 0.95 ± . B = 5 T. The large degree of polarization correlation(higher than that at zero field) shows that probability ofspin-flip accompanied transition between the intermedi-ate excitonic states of the cascade decreases when X level H/H raw counts C oun t s H/H: 5.26 V/V: 5.23 H/V: 0.37 V/H: 0.47 (a) N o r m a li ze d c oun t s i n p ea k -20 0 20 40 6001234567 / : 0.08 / : 6.71 / : 6.93 / : 0.41(c) : 2.85: 2.71 : 2.69 : 2.81(b) N o r m a li ze d c oun t s i n p ea k = t X t XX (ns) FIG. 4: (Color online) Polarized crosscorrelation of the XX and X emission. Each panel contains histograms for four pos-sible polarization combinations of the photon pair. Polariza-tions of correlated transitions are indicated in XX / X order.Points represent integrated counts in a peak, normalized tothe average value for large delays. Solid lines are guides tothe eye. Magnitudes of zero delay peaks in respective his-tograms are given in the each panel. Polarization correlationof photons from XX - X cascade is evidenced in linear H/Vpolarization basis at B = 0 T (a) and in circular σ + /σ − polarization basis at B = 5 T (c). There is no polarizationcorrelation in circular σ + /σ − polarization basis at B = 0 T(b). Panel (a) shows additionally a raw coincidence countshistogram (left axis). splitting increases in magnetic field. Calculation of theexciton relaxation time at B = 5 T (simple exciton spin-flip time in this case) made under assumption that X life-time does not change in the magnetic field and includinga correction for incomplete (98.3%) circular polarizationof excitonic states, yields the value T X = 16 ± XX - X crosscorrelations mea-sured (Fig. 4) shows that pairs of photons emittedfrom an anisotropic QD in XX - X cascade exhibit at B = 0 T only a strong classical correlation in the lin-ear polarization basis corresponding to symmetry axes ofthe dot, in agreement with previous experiments. Anisotropy induced collinear polarization correlation ofphotons emitted in XX - X cascade is converted to acounter-circular polarization correlation after applyingmagnetic field parallel to the sample growth axis. Ex-citon spin relaxation is found to be slowed down in thepresence of magnetic field, as demonstrated by increase ofthe X spin relaxation time from 3 . ± . B = 0 Tto 16 ± B = 5 T. C. Single carrier spin memory effects
Previous investigations of QD emission by polar-ization resolved correlation spectroscopy have beenlimited to the XX - X cascade, which was found toproduce polarization-correlated or polarization-entangled triggered photon pairs. In this section,we present results of time and polarization resolved corre-lations between charged exciton and neutral exciton pho-tons emitted from a single CdTe/ZnTe QD. We examinethe influence of magnetic field on the carrier spin dy-namics. The measurements revealed long lasting carrierspin memory in magnetic field and confirmed an effectivecarrier spin read-out .The measurements were performed in the linear orin the circular polarization basis. The results of CX - X crosscorrelation involving CX and X emission measuredat B = 0 T in the circular polarization basis are presentedin Fig. 5(a). All the histograms in Fig. 5(a) have theircentral peak strongly suppressed and exhibit an asym-metric shape, characteristic for CX - X crosscorrelation.This is known to originate from the QD charge state vari-ation under nonresonant excitation, which favors captureof single carriers instead of entire excitons. The centralpeak of the CX - X histogram (Fig. 5) represents the de-tection of pairs consisting of CX and X photons emittedfollowing the same excitation pulse, therefore its suppres-sion reflects expected antibunching of CX and X photons.Peaks at a negative (positive) delay represent pairs ofphotons detected following different pulses, such that X photon precedes (succeeds) CX photon. The dependenceof circular polarization of X emission on circular polar- (a) B = 0 T -20 0 20 40 600.00.51.01.52.0 B = 5 T / / / / (b) = t X t CX (ns) N o r m a li ze d c oun t s i n p ea k FIG. 5: (Color online) Histograms of CX - X crosscorrelationmeasured in the circular σ + /σ − polarization basis for fourpossible combinations of the polarization of the CX - X photonpair (a) at B = 0 T and at (b) B = 5 T. Polarizations ofcorrelated transitions are indicated in CX / X order. Pointsrepresent integrated and normalized (to the average at largedelays) number of counts in a peak. Solid lines are guides tothe eye. Values given in panels represent normalized numberof counts in m = 1 peak of a respective histogram. Excitationpower at I XX /I X = 0 .
30 (see Sec. IV). Enhanced m = 1peaks in the case of correlation between orthogonal CX and X polarizations indicate transfer of spin orientation from CX to X over time of the repetition period (b). ization of previously emitted CX photon ( m > CX thatrecombined affects the spin orientation of subsequentlyformed X . In such a case the carrier present in the dot af-ter CX recombination would provide transfer of the spinpolarization from CX to X . Its spin state would be read from the polarization of X emission. However, no depen-dence of peak intensity on combination of photon pair po-larizations in neither circular (Fig. 5(a)) nor linear H/V(not shown) polarization bases is observed at B = 0 T. We deduce therefore that polarization of the carrier leftin the dot after CX recombination is not transferred tothe X photon subsequently emitted by the QD. This maybe caused by the anisotropic exchange splitting of the X state, resulting in the averaging out of the circular po-larization by precession between two linearly polarizedeigenstates. For the same reason, no optical orientationof excitons is observed in anisotropic quantum dots. However, the polarization transfer becomes significanton application of magnetic field, when both CX and X emit in common circular σ + /σ − polarization basis. At B = 5 T peaks at small positive delays show a signif-icant enhancement or suppression for opposite or equalcircular polarizations, respectively (Fig. 5(b)). The firstpeak at positive delay ( m = 1 peak), represents X photondetection in the pulse immediately following the detec-tion of CX photon. Its normalized areas are 1 . ± . . ± . . ± .
05 and 0 . ± .
05 for photons of the same polar-ization. This is an evidence of spin memory in magneticfield.The intensities of the m = 1 peaks in Fig. 5(b) corre-spond to polarization degree of 39%. Further ( m > CX - X histogram also show a polarization,which decreases with increasing peak number. This oc-curs because each additional excitation pulse reduces theprobability that the dot remains in the original, post CX recombination, single carrier spin state.In summary, the results of CX - X crosscorrelation inmagnetic field provide a clear evidence of the polarizationmemory extending over a few excitation pulses and ofeffective optical read-out of the single carrier spin in thedot. IV. MODEL DESCRIPTION OF THEPOLARIZED CX - X CROSSCORRELATION
As already mentioned, the singlet ground state of thecharged exciton contains two identical carriers of oppo-site spins. One of them decays in CX recombination,emitting a photon with circular polarization determinedby its spin. The spin polarization of the second carrierwill determine the polarization of an X photon emittedduring X recombination after next laser pulse. This willhappen after trapping a carrier of opposite charge. Ifthe spin polarization is conserved over the repetition pe-riod, the CX and X photons produced by two consecutivepulses will thus have opposite circular polarizations. Inreality, this spin conservation is never perfect and canbe measured by polarization correlation coefficient P de-fined as P = I σ − /σ + + I σ + /σ − − I σ + /σ + − I σ − /σ − I σ − /σ + + I σ + /σ − + I σ + /σ + + I σ − /σ − (1)where I γ/δ denotes intensity of the correlated counts inthe CX - X histogram measured with CX and X photonsdetected in polarizations γ and δ , respectively. P o l a r i za ti on P ( m ) ( % ) Pulse number m P ( m ) exp P ( m ) calc B = 5 T
FIG. 6: (Color online) Polarization correlation versus pulsenumber at B = 5 T. Experimental values (squares) are com-pared with calculation (dots). Model parameters α = 0 . β = 0 . ξ = 0 . κ = 0 .
69 (see text). Excitation powerat I XX /I X = 0 .
26. Lines added to guide the eye.
In the experiment we measure P ( m ) exp values related toconsecutive peaks of the CX - X histogram, expressed bytotal correlated counts I ( m ) γ/δ of respective peaks, num-bered by index m . Values of P ( m ) exp determined for peaksof 1 ≤ m ≤ P ( m ) is equivalent to the ratio of the probability that X photonwith polarization defined by the carrier spin conservationis emitted following the m -th pulse to the overall prob-ability of X photon emission following the m -th pulse.Thus, P ( m ) can be written taking into account differentpolarization loss mechanisms. E.g., for m = 1 peak: P (1) calc = ǫ n (1) X n (1) X + n (1) XX T X T X + τ radX κ (2)where symbols n ( m ) i denote occupation probability of QDstates directly after an excitation pulse, which is assumedto be short enough to neglect recombination during ex-citation (see discussion further below). The upper indexgiven in parentheses encodes the pulse number m , whilethe lower index i encodes the dot state. Factor ǫ (inthe case of selected QD estimated at 96.2% at B = 5 T)represents the impact of elliptical polarization of the exci-tonic eigenstate. The fraction with XX and X occupationprobabilities represents polarization loss due to biexcitonrecombination channel, where no polarization is trans-ferred by the singlet XX state. Since T X is X spin-fliptime (see Sec. III B), expression T X /( T X + τ radX ) repre-sents the loss of the exciton spin polarization during itslifetime. Finally, κ represents other possible loss mech-anisms. In particular, it could be a spin-flip of the re-maining carrier. However, we checked that magnitude ofthe peaks in the polarized CX - X correlation histogramremains unchanged after doubling of the excitation repe- tition period (not shown). This indicates a negligible car-rier spin relaxation over the timescale comparable withthe repetition period. A possible polarization loss during X state formation by capture of a second carrier of anopposite charge will be also found negligible (see discus-sion in the following). Hence, the respective polarizationloss results from an interaction of the confined electronwith non-equilibrium population of carriers (exchange in-teraction) and/or phonons (possible local heating of thesample) excited by laser pulses.The timescale of the observed memory effect mightalso suggest that CX recombination leaves in the dot anelectron and not a hole. In contrast to the case of theelectron, the spin relaxation of the hole is known to berelatively fast, occurring in the time of the order com-parable with the repetition period of probing the carrier’sspin state in our experiment. Thus, we make tentativeassumption that CX is negatively charged.We shall also comment on the influence of dark excitonformation on excitonic polarization degree. Dark, nonra-diative exciton state is formed in the case when carrier iscaptured by the dot already containing a carrier of oppo-site charge and the same spin. After a spin-flip processthe dark exciton converts into a bright state and decaysradiatively. Such an excitonic luminescence could lowerthe effective excitonic PL polarization degree. However,the time constant of dark exciton spin-flip is large com-pared to the excitation repetition period. This is knownfrom the comparison between the results of unpolarized CX - X crosscorrelation measurements performed with twodifferent repetition periods. They reveal no significantdifference in intensity of peaks of the same number in twohistograms. Thus, the influence of the dark exciton for-mation on exciton polarization degree can be neglectedand it was not taken into account in the construction ofthe model describing experimental data.The measured polarization may be understood as aproduct of carrier spin polarization reduced by read-out efficiency (first two factors in Eq. 2) and loss mecha-nisms (last two factors in Eq. 2). In order to determinethe most prominent factors lowering the measured po-larization we introduce a simple rate equation model. Itallows us to compute the occupation probabilities nec-essary for calculation of P ( m ) calc . We consider a ladder ofstates involving five states: from the empty dot to thebiexciton state. Since only one charged exciton line ofsignificant intensity is observed, we neglect states of op-posite charge (corresponding weak trion line visible inFig. 1 at 2217 meV). We define a set of variables n ( m )0 , n ( m ) e , n ( m ) X , n ( m ) CX , n ( m ) XX describing the occupation of lev-els (encoded by the lower index) just after the excitationby the m -th pulse is finished. It is known from indepen-dent measurements on the same sample that the effec-tive excitation pulse duration ( ∼
20 ps) is much shorterthan radiative decay times (hundreds of ps), therefore weneglect recombination during the excitation process. Ex-citation through capture of single carriers of both signsand entire excitons with respective time dependent rates α ( t ) = α · f ( t ), β ( t ) = β · f ( t ), and ξ ( t ) = ξ · f ( t ), isassumed. A common normalized excitation pulse shape f ( t ) is assumed ( R T rep f ( t )d t = 1), while α , β , ξ repre-sent time-integrated capture rates per pulse. Escape ofthe carriers out of the dot is not taken into account as ithas been shown to be negligible. Our simulations showthat within the assumptions of the model, the shape f ( t )of the excitation pulse is not important. We describe theexcitation process with the following set of rate equa-tions: d n ( m )0 d t = − ( α ( t ) + ξ ( t )) n ( m )0 (3a)d n ( m ) e d t = α ( t ) n ( m )0 − ( β ( t ) + ξ ( t )) n ( m ) e (3b)d n ( m ) X d t = ξ ( t ) n ( m )0 + β ( t ) n ( m ) e − ( α ( t ) + ξ ( t )) n ( m ) X (3c)d n ( m ) CX d t = ξ ( t ) n ( m ) e + α ( t ) n ( m ) X − β ( t ) n ( m ) CX (3d)d n ( m ) XX d t = ξ ( t ) n ( m ) X + β ( t ) n ( m ) CX (3e)We assume purely radiative decay of excitons. Thus, theinitial conditions for a consecutive excitation pulse aredetermined by the final state of excitonic recombinationafter preceding excitation pulse. For the particular caseof m = 1, the initial conditions are in a good approxi-mation n (1) e (0) = 1 and n (1) i = e (0) = 0 (single carrier leftafter CX recombination present in the dot). Integratedcapture rates α , β , ξ obtained from the experiment onthe same QD with no polarization resolution were used. They were scaled by a common factor in order to takeinto account a variable excitation power. The factor wasadjusted to fit the ratio of XX to X emission intensity( I XX /I X ). (Consistently with Ref. 16, α / β / representscapture rate of the first /the second/ carrier to the dot,that is electron /hole/.)The first consequence of the model is the variation ofthe calculated polarization coefficient P with the excita-tion power. Also the P (1) exp decreases with the increasingexcitation power. This is expected, since the contributionof X photons coming from XX radiative decay increaseswith the excitation intensity. They are effectively unpo-larized and they lower the value of P ( m ) exp . We determined P (1) calc for different excitation powers by solving Eqs. 3with suitably scaled rates α , β , and ξ assuming full con-servation of the electron spin ( κ = 1). The Figure 7(a)shows comparison of P (1) calc for κ = 1 and P (1) exp plottedas a function of the I XX /I X ratio. The ratio I XX /I X was chosen to represent excitation power, since it pro-vides a convenient measure of excitation intensity. Thediscrepancy between the experimental and the calculatedvalues is a clear indication that conservation of the elec-tron spin polarization between the CX and X emissionsis not perfect.Thus, we fitted P (1) calc to P (1) exp with κ being the (only)fitting parameter. Values of κ determined this way areshown in Fig. 7(b) as a function of I XX /I X ratio. Asvisible in the Fig. 7(b), κ attains the value of κ = 0 . I XX /I X = 0 .
26 and decreases with the increasingexcitation power. A linear fit to the experimental pointsis also shown in the Fig. 7(b). The electron polarizationconservation, and the electron spin optical read-out arealmost perfect in the limit of low excitation power.This means that the capture of the hole to form anexciton with the electron in the QD does not induce anysignificant polarization loss, since process of X formationdoes not depend on excitation power. The dependenceof κ on the excitation intensity confirms that κ origi-nates from the factors such as interaction of the confinedelectron with carriers and/or phonons generated by theexcitation pulse, as contribution of these factors dependson the excitation power.Therefore, the loss of the electron polarization repre-sented by κ takes place following each excitation pulse.This allows us to write down P ( m ) calc for consecutive pulsesin the form: P ( m ) calc = ( n (1) e ) m − ǫ n (1) X n ( m ) X + n ( m ) XX T X T X + τ radX κ m (4)The factor ( n (1) e ) m − reflects the probability that QDkeeps its one-carrier state unchanged through m − κ m represents degree of con-servation of the electron spin following m consecutive ex-citation pulses. Its exponential dependence on the peaknumber m (evidenced by Fig. 6) confirms the role of laserpulses as the source of polarization loss described by κ .Integration of Eqs. 3 yielded probabilities n ( m ) i of find-ing the dot in a state i following m -th excitation pulse.Thus P ( m ) calc for consecutive pulses were calculated fromEq. 4. They are compared with the experimental valuesof P ( m ) exp for peaks of 1 ≤ m ≤ I XX /I X = 0 .
26. The satisfactory agreementbetween calculated and experimental values justifies theintroduced model.To summarize this Section, CX - X crosscorrelationmeasurements provide evidence for single carrier spin po-larization memory in magnetic field. We described quan-titatively the polarization memory after consecutive ex-citation pulses. Comparison between the model and theexperiment shows that carrier spin conservation and theoptical read-out efficiency are close to 100% in the limitof low excitation power. The maximum efficiency of thespin read-out obtained in the experiment is 68%. The CX - X crosscorrelation performed for different excitation P o l a r i za ti on P ( ) ex p ( % ) pulse number: m = 1(a) (b) I XX / I X FIG. 7: (a) Polarization correlation at B = 5 T for the firstpulse after CX emission P (1) exp versus excitation power repre-sented by the ratio I XX /I X . Solid line – calculation ( κ = 1)according to Eq. 2. (b) Coefficient κ of carrier spin conserva-tion at B = 5 T determined from fitting of the P (1) calc to P (1) exp for different excitation powers. powers allowed us to verify the expected influence of biex-citon formation on the loss of polarization memory. V. CONCLUSIONS
We performed polarized crosscorrelation measure-ments of photons from exciton, biexciton, and trion re- combination in a single, anisotropic CdTe/ZnTe quantumdot. In absence of magnetic field we observed a strongcollinear polarization correlation ( χ HV = 0 . ± .
06) ofphotons emitted in the biexciton-exciton cascade. WhenZeeman splitting dominates over anisotropic exchangesplitting, the photons in the cascade become correlatedin opposite circular polarizations ( χ σ + σ − = 0 . ± . T X = 3 . ± . B = 0 T and 16 ± B = 5 T were determined fromthe XX - X correlation measurements.Trion-exciton crosscorrelation measurements con-ducted in magnetic field of 5 T have revealed longtimescale (at least tens of ns) polarization memory inthe QD excitonic emission. Effective optical read-out ofthe spin polarization of a single carrier confined in theanisotropic QD has been demonstrated in magnetic field.The decay of the polarization memory with the increas-ing number of excitation pulses separating two correlatedphotons has been described with a simple rate equationmodel. It was attributed to the combined influence ofcompetitive biexciton spin singlet recombination and lossof carrier spin polarization, perturbed primarily by thevery laser light used for the spin read-out . Efficiency ofoptical read-out of the spin in magnetic field turned outto be dependent on the excitation power (the maximumefficiency obtained in the experiment was 68%).The results obtained indicate CdTe/ZnTe QDs as avaluable proving ground for future applications of polar-ization controlled single photon emitters or spin qubitsin the area of quantum information processing. Acknowledgments
This work was partially supported by the Polish Min-istry of Science and Higher Education research grants inyears 2005-2010 and by European project no. MTKD-CT-2005-029671. ∗ Electronic address: Jan.Suff[email protected] M. Paillard, X. Marie, P. Renucci, T. Amand, A. Jbeli,and J. M. G´erard, Phys. Rev. Lett. , 1634 (2001). A. V. Khaetskii and Y. V. Nazarov, Phys. Rev. B ,12639 (2000). M. Ikezawa, B. Pal, Y. Masumoto, I. V. Ignatiev, S. Y.Verbin, and I. Y. Gerlovin, Phys. Rev. B , 153302(2005). I. A. Akimov, D. H. Feng, and F. Henneberger, Phys. Rev. Lett. , 056602 (2006). M. Kroutvar, Y. Ducommun, D. Heiss, M. Bichler,D. Schuh, G. Abstreiter, and J. J. Finley, Nature ,81 (2004). S. Cortez, O. Krebs, S. Laurent, M. Senes, X. Marie,P. Voisin, R. Ferreira, G. Bastard, J.-M. G´erard, andT. Amand, Phys. Rev. Lett. , 207401 (2002). A. Ebbens, D. N. Krizhanovskii, A. I. Tartakovskii,F. Pulizzi, T. Wright, A. V. Savelyev, M. S. Skolnick, and
M. Hopkinson, Phys. Rev. B , 073307 (2005). R. J. Young, S. J. Dewhurst, R. M. Stevenson, P. Atkinson,A. J. Bennett, M. B. Ward, K. Cooper, D. A. Ritchie, andA. J. Shields, New J. Phys. , 365 (2007). P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M.Petroff, L. Zhang, E. Hu, and A. Imamoˇglu, Science ,2282 (2000). E. Moreau, I. Robert, J. M. Gerard, I. Abram, L. Manin,and V. Thierry-Mieg, Appl. Phys. Lett. , 2865 (2001). G. Bennet and C. H. Brassard, Proceedings of IEEE Int.Conf. on Computers, Systems and Signal processing, Ban-galore, India , 175 (1984). A. K. Ekert, Phys. Rev. Lett. , 661 (1991). D. J. P. Ellis, R. M. Stevenson, R. J. Young, A. J. Shields,P. Atkinson, and D. A. Ritchie, Appl. Phys. Lett. ,011907 (2007). A. Kudelski, K. Kowalik, A. Golnik, G. Karczewski,J. Kossut, and J. A. Gaj, J. Lumin. , 127 (2005). K. Kowalik, A. Kudelski, A. Golnik, J. A. Gaj, G. Kar-czewski, and J. Kossut, Acta Phys. Pol. A , 539 (2003). J. Suffczy´nski, T. Kazimierczuk, M. Goryca, B. Piechal,A. Trajnerowicz, K. Kowalik, P. Kossacki, A. Golnik, K. P.Korona, M. Nawrocki, J. A. Gaj, and G. Karczewski, Phys.Rev. B , 085319 (2006). G. Karczewski, S. Ma´ckowski, M. Kutrowski, T. Wojtow-icz, and J. Kossut, Appl. Phys. Lett. , 3011 (1999). J. Jasny and J. Sepio l, Chem. Phys. Lett. , 439 (1997). R. Hanbury-Brown and R. Q. Twiss, Nature , 27(1956). L. Besombes, K. Kheng, and D. Martrou, Phys. Rev. Lett. , 425 (2000). C. Santori, D. Fattal, M. Pelton, G. S. Solomon, and Y. Ya-mamoto, Phys. Rev. B , 045308 (2002). T. Flissikowski, A. Hundt, M. Lowisch, M. Rabe, andF. Henneberger, Phys. Rev. Lett. , 3172 (2001). S. Ma´ckowski, T. A. Nguyen, H. E. Jackson, L. M. Smith,J. Kossut, and G. Karczewski, Appl. Phys. Lett. , 5524(2003). R. M. Stevenson, R. M. Thompson, A. J. Shields, I. Farrer,B. E. Kardynal, D. A. Ritchie, and M. Pepper, Phys. Rev.B , 081302(R) (2002). S. M. Ulrich, S. Strauf, P. Michler, G. Bacher, andA. Forchel, Appl. Phys. Lett. , 1848 (2003). L. Besombes, L. Marsal, K. Kheng, T. Charvolin, L. S.Dang, A. Wasiela, and H. Mariette, J. Cryst. Growth , 742 (2000). R. J. Young, R. M. Stevenson, P. Atkinson, K. Cooper,D. A. Ritchie, and A. J. Shields, New J. Phys. , 29 (2006). R. M. Stevenson, R. J. Young, P. Atkinson, K. Cooper,D. A. Ritchie, and A. J. Shields, Nature , 179 (2006). N. Akopian, N. H. Lindner, E. Poem, Y. Berlatzky,J. Avron, D. Gershoni, B. D. Gerardot, and P. M. Petroff,Phys. Rev. Lett. , 130501 (2006). K. Kowalik, O. Krebs, A. Lemaitre, B. Eble, A. Kudelski,P. Voisin, S. Seidl, and J. A. Gaj, Appl. Phys. Lett. ,183104 (2007). T. Flissikowski, I. A. Akimov, A. Hundt, and F. Hen-neberger, Phys. Rev. B , 161309(R) (2003). K. Korona, P. Wojnar, J. Gaj, G. Karczewski, J. Kossut,and J. Kuhl, Solid State Commun.133