Electron spin polarization and detection in InAs quantum dots through p-shell trions

Transcription

1 PHYSICAL REVIEW B 81, Electron in olarization and detection in InA quantum dot through -hell trion S. G. Carter, Ş. C.Bădecu, and A. S. Bracker Naval Reearch Laboratory, Wahington, DC , USA Received 16 Setember 29; revied manucrit received 1 November 29; ublihed 8 January 21 We erform two-color time-reolved ectrocoy of in dynamic in an enemble of InA quantum dot, demontrating that an electron in olarization in negatively charged quantum dot can be efficiently generated or detected with ule tuned to -hell trion. Due to the olarization election rule and exchange litting of the electron in trilet and inglet trion tate, the abortion robability of circularly olarized light deend trongly on the in tate of the reident electron in the quantum dot. Thi lead to in elective excitation of electron to the -hell trion tate, generating a in olarization in the enemble of unexcited reident electron. Maniulating in tate through the excited trion tate allow for earation of the excitation wavelength from the emiion wavelength for control of the atial extent of the excited-tate wave function. DOI: 1.113/PhyRevB PACS number: Hc, D, Fe I. INTRODUCTION An electron or hole in in a emiconductor quantum dot QD i a trong candidate a a quantum bit for quantum information alication. Otical maniulation of in tate ha been of articular interet ince it can be erformed on ultrafat time cale, it coule the in qubit to hoton qubit, and it can ectrally or atially elect different QD. Much of the reviou work in thi area ha relied on the lowet charged exciton trion tate, in which an electronhole air i generated in the conduction and valence hell of the QD. Reonant or near-reonant excitation of thi lowet-energy trion tate ha been quite roductive, with everal recent demontration of in-tate initialization, 1,2 timereolved ingle-in detection, 3 and fat in rotation. 4 6 Uing excited trion tate can rovide additional flexibility and functionality. One advantage of otical maniulation with excited tate i that the wavelength of the excitation laer i well earated from the QD emiion wavelength, reventing cattered laer light from overwhelming emiion. 7 Another benefit of uing excited tate i having multile tranition with different function. In the couled QD ytem of Ref. 8, ue of the trilet trion tate excited in tate wa eential to roduce a lambda ytem for in maniulation a well a cycling tranition for readout. Alo, control of the orbital wave function through excited tate can be ued to control couling to nearby QD. A recent theoretical tudy howed that the extended orbital wave function of excited-tate trion can be ued to entangle two electron in in two nearby QD that are uncouled in the ground tate. 9 In thi work, we how that articular excited trion tate in ingle QD, -hell trion with an -hell electron, a -hell electron, and a -hell hole, can be ued to maniulate and detect electron in tate. There have been a number of reviou tudie of the excited trion tate in QD uing hotoluminecence PL. 7,1 19 Thee tudie give information on the energie and olarization of the different tranition, and many have been able to infer a reident electron in olarization baed on luminecence olarization. A few tudie have alo meaured the time-reolved carrier dynamic 11,12,17,19 and temoral correlation of emitted hoton. 7,14 Thee time-reolved luminecence tudie rovide information on trion dynamic and relaxation but do not directly meaure the reident electron in tate. Uing two-color time-reolved Faraday rotation and elliticity TRFR and TRFE, we directly olarize and robe the reident electron in in an enemble of InA QD uing the -hell trion tate. A circularly olarized um ule referentially excite QD with a articular reident electron in olarization ee Fig. 1a and 1b. After excitation the reident electron in unexcited QD are then rimarily of the ooite in orientation. A linearly olarized robe ule meaure thi reident in olarization, which recee in the alied magnetic field a a function of robe delay. Sin electivity come from the olarization election rule of the -hell trion tate and the ignificant electron-electron exchange litting between the trilet and inglet tate. We oberve thi electivity by examining TRFR and TRFE a a function of um and robe hoton energy. When the robe (a) hell excitation Conduction + inglet + Valence + (b) hell excitation inglet, trilet Pauli blocked + trilet FIG. 1. Color online Electron- and hole-energy level in a quantum dot, howing in electivity in the excitation of a -hell trion and b -hell trion for different initial in tate. Sin electivity i rovided by Pauli blocking in the hell and by different energie and diole moment of inglet and trilet tate in the hell /21/814/ The American Phyical Society

2 CARTER, BĂDESCU, AND BRACKER (a) = um robe. At the center of the PL, the robe rimarily hould be tuned to -hell trion. An external magnetic field of 2 T i alied erendicular to the otical axi Voigt geometry in order to oberve receion of the electron in. For degenerate um robe =, where both are rimarily tuned to -hell trion, there are three different comonent due to neutral exciton, trion, and electron. The neutral exciton from uncharged QD give the har ignal near zero delay followed by a heavily damed ocillation due to the aymmetric exchange litting. Trion give a imle exonential decay due to the lifetime of 5, and electron in give the clear ocillating ignal at 12 GHz due to receion in the magnetic field. Puming at higher energie near the -hell um =32 mev give imilar behavior with a maller amlitude. One might alo exect to oberve dynamic of the excited trion tate when uming at high hoton energie. Signal from the excited tate may aear very imilar to the neutral exciton and trion comonent, and many of the excited tate relax quickly to the hell, making it difficult to ditinguih between them. Here, we focu excluively on the ignal due to receing electron in. Interetingly, thi ignal i due to electron that are not excited by the um ule. The um ule referentially excite trion in quantum dot when the reident in i of a articular orientation. Electron in in the unexcited QD are left with the ooite orientation. One might exect that trion recombination will trongly affect thi electron in olarization. However, in a ignificant Voigt magnetic field, receion of the electron in during the trion lifetime mean that recombination return the electron in with a random hae comared to unexcited receing electron in. The effect of recombination on the electron in olarization thu average out to zero, leading to a long-lived electron in olarization The inglez (b) y x QD amle um Bfield hoton energy i fixed at the -hell trion and the um i canned to higher hoton energie, a clear eak in the in olarization i oberved at the exected -hell trion energy. We alo fix the um at the -hell trion and can the robe to oberve a eak in the detection of the in olarization at the -hell trion. Thee reult are a te toward greater functionality in otical control of in tate in quantum dot. II. EXPERIMENT robe FIG. 2. Color online a Photoluminecence of the quantum dot. The vertical line rereent the um and robe. b Exerimental geometry for um-robe exeriment. The QD amle conit of 2 layer of InA QD, grown by molecular-beam eitaxy through Stranky-Kratanov elfaembly. The QD are artially caed with GaA and the remaining InA i fluhed away to roduce a truncated dik tructure of height 2.5 nm and lateral dimenion of 1 2 nm. 2 The QD layer are earated by 3 nm GaA barrier, and the QD areal denity er layer i etimated at cm 2. The amle i n doed with tellurium, making a ignificant fraction of the QD charged with a ingle electron. Figure 2a dilay the PL of the QD at 5 K, with a full width at half maximum of 5 mev due to varying QD ize. Emiion from the -hell tate cannot be reolved due the large energy variation in the -hell tate. Uing um-robe TRFR and TRFE Fig. 2b, thee -hell tate can be reolved. The um-induced rotation or elliticity of a linearly olarized robe ule meaure only thoe QD with energy level near the robe hoton energy, which ha a bandwidth of 1 mev 1.8 ule length. Elliticity rotation correond to a difference in the amlitude hae of the + and comonent of the tranmitted robe, giving enitivity to in. A circularly olarized um ule alo with a bandwidth of 1 mev can only affect the robe olarization when the um i reonant with energy level of the ubet of QD meaured by the robe. The delay of the robe relative to the um give icoecond time reolution, and the ule are reeated at a rate of 81 MHz. The um robe ule i focued down to a diameter of 8 m 5 m with an average intenity of 6 W/cm W/cm 2. Thee intenitie are ket well below aturation in order to avoid comlicating effect uch a mode locking 21 and the accomanying nuclearin olarization effect that have reviouly been oberved in thi QD amle. 22 Figure 3a dilay the TRFE with the robe at a hoton energy of ev for two different um detuning um rad) Elliticity ( ). amlitude (rad) Ellit./Rot (a) (b) Probe fixed um =32meV um = mev robe = ev Probe delay () Rotation Elliticity -5 robe = ev Pum detuning (mev) PHYSICAL REVIEW B 81, (c) (d) Pum fixed robe =32meV robe =mev um = ev Probe delay () Rotation Elliticity um = ev Probe detuning (mev) FIG. 3. Color online a and c TRFE ignal v robe delay for degenerate um robe and for a detuning of 32 mev. b and d TRFR and TRFE amlitude v um/robe detuning. The robe i fixed at robe =1.326 ev for a and b, and the um i fixed at um =1.326 ev for c and d

3 ELECTRON SPIN POLARIZATION AND DETECTION IN PHYSICAL REVIEW B 81, Probe hoton energ gy(mev) Pumhoton energy (mev) in coherence time in thi amle ha reviouly been meaured to be 1 2 n at 3 T. 22 The oberved decay time of 6 in Fig. 3a i due to inhomogeneity of the g factor in the QD enemble. Signal at negative delay due to mode locking are weak at the low ower ued in thee exeriment and have only been oberved when uming in the hell. Additionally, no obviou ignature of nuclear-in effect have been oberved under thee condition. Both the TRFE and TRFR are meaured for a erie of um detuning from the fixed robe, and the electron in comonent i fitted to an exonentially decaying coine. The amlitude are lotted in Fig. 3b, dilaying a trong reonance near zero detuning, a weaker reonance at 3 mev, and feature at higher energie tarting at 5 mev. The TRFR how eentially the ame feature a TRFE but with dierive feature intead of abortive. The focu of the dicuion i on the TRFE a it give a imler ectrum while the TRFR amlitude rovide a comlementary ectrum that i antiymmetric about each reonance. 22 The zero detuning reonance i due to excitation of the -hell inglet trion and it width 1.7 mev correond to the ectral overla of the um and robe. We attribute the reonance at 3 mev to the -hell inglet and trilet trion tate. The reonance i quite broad 8 mev due to variation in the - litting but the integrated ignal i roughly the ame a for the -hell reonance. The decay time and hae of the electron in ignal are about the ame when uming in the hell or hell, a een in Fig. 3a. The higher energy feature, which tend to blur together to form a continuum, will not be dicued here. We alo how that the electron in tate can be robed through the -hell trion in Fig. 3c and 3d, for which the um i now fixed in the hell at ev. The TRFE ignal v robe delay i lotted in Fig. 3c with the robe in the hell robe = robe um = and in the hell robe =32 mev. The electron in ignal i maller when robing in the hell but ha a imilar hae and decay time. Figure 3d dilay the ectral deendence of the robe. There i a trong -hell reonance near the um and a weaker -hell reonance 32 mev higher, with much le ignal at higher energie. The ability to robe the electron in tate through the hell i oible for the ame reaon in olarization i oible: electron in elective trion tranition with circularly olarized light. An electron in olarization reult in more abortion refraction for onehoton helicity than the other, reulting in elliticity rotation of the linearly olarized robe. By varying both the um and robe hoton energie taking time-reolved can at each um/robe combination, we roduce a two-dimenional 2D ma of the excitation and detection of the reident in olarization. Thi ma, dilayed in Fig. 4, i lower reolution than the can in Fig. 3b and 3d, but the main feature are clear. The ignal i tronget along the diagonal, for which the um and robe are degenerate. Parallel to the diagonal but at a robe energy 3 mev higher i a weaker ignal, which correond to uming the electron in through the -hell trion and robing through the -hell trion. There i alo a arallel feature about 3 mev below the diagonal, which correond to uming electron in through the -hell trion and robing through the -hell trion. Thi feature i urrounded by a near continuum, articularly for the highet um hoton energie. At thee energie, the um can excite into multile excited trion tate, o the robe can detect electron in over a wide range of energie, including both the -hell and -hell trion. III. ANALYSIS To undertand the origin of the electron in olarization and detection, conider the energy level of a negatively charged QD. Figure 5 how the electron in tate e, the trion tate, and the allowed tranition between them for + excitation. The lowet trion tate i an electron inglet with both electron in the -orbital tate S. The next trion tate, labeled i otically forbidden for QD with inverion ymmetry a it excite one carrier either electron or hole to Elliticity y amlitude (rad) FIG. 4. Graycale intenity ma of the TRFE amlitude v um and robe hoton energie. The horizontal and vertical dahed line rereent the can taken in Fig. 3b and 3d. The intenity cale i aturated for many oint along the diagonal o that low intenity oint can be een. S T S e FIG. 5. Color online Energy level of a negatively charged QD with the electron and hole energie hown earately to the left. The trion level are divided left and right by the hole orientation, and. Arrow how allowed tranition for + excitation with the in tate oriented along the otical axi

4 CARTER, BĂDESCU, AND BRACKER the hell and one to the hell. The next excited tate T,S contain one electron in the hell, one electron in the hell, and a hole in the hell. The earation energy from the S i dominated the ingle-article quantization energie of an electron and a hole. Thee excited tate can have an electron-electron trilet T or inglet S in tructure, with a earation between them given by the electron-electron exchange energy ee. The trilet tate have a fine tructure due to the reence of electron-hole exchange. Thi diagram dilay the electron in tate oriented along the otical axi z to imlify the election rule. Thi icture work well during the excitation roce ince the ule length 2 i much horter than the electron receion eriod 83. We make the aumtion for all of the trion tate that only the in-elective excitation generate the electron in olarization. Excitation of a trion in a QD deolarize the reident electron in after recombination. The electron in olarization come from QD that are not excited by the ule. Thi i in contrat to everal tudie in which circularly olarized excitation in the wetting layer or barrier layer reulted in in olarization. 12,17 19,26,27 In thee reviou exeriment, excitation did not deend on the in orientation of the reident QD electron. Rather, relaxation and recombination of the in-olarized, otically excited carrier reulted in a reident in olarization. Thee exeriment were erformed either without a magnetic field, with a Faraday magnetic field, or with a very mall Voigt magnetic field, none of which lead to ignificant in receion during recombination. For a trong Voigt magnetic field, recombination hould leave electron in unolarized We alo aume the electron in are unolarized before each um ule. For individual in thi aumtion may be invalid ince the individual in coherence time i longer than the ule reetition eriod. However, the enemble in olarization i nearly zero before each ule due to inhomogeneity in the in receion frequency, giving no ignificant negative delay ignal in Fig. 3a. Thee aumtion greatly imlify calculation of the electron in olarization. The degree of in olarization for a QD i only determined by the robability of the laer ule to excite a in-u electron v a in-down electron, w,n w,n, where n i a articular trion tate. Thee excitation rate are determined by the trion linewidth n, by the ectral ditribution of the laer taken below a Gauian, and by the diole matrix element n of the tranition 28 w,n w,n de 2 /2 2 n,n 2,n 2 n 2 + n 2. 1 The ectral width and center of the laer ule are and, reectively. If the rocee that eliminate from the enemble dominate n w,n n w,n then the olarization i in down. When n w,n n w,n there are more tate eliminated from the enemble and the olarization i in u. Conider the in-election rule for each of the trion tate in Fig. 5. Clearly for the -hell inglet trion S,a + ule only excite, giving a in-down olarization. The trilet -hell trion T conit of three cloely aced olarization Avg. in (a) total S T Energy (mev) PHYSICAL REVIEW B 81, (b) T T Energy (mev) olarization Avg. in Sin elec ctivity FIG. 6. Color online a Average reident electron in olarization generated through -hell trion tate for a ubenemble of identical QD. b Average reident electron in olarization and in electivity for -hell and -hell trion in an inhomogeneou enemble. Energie are relative to the -hell trion S. Selectivity i only lotted for energie where there i ignificant trion abortion. tate lit by the electron-hole exchange interaction eh 2 ev, 15 T +, T, and T, with the ubcrit, correonding to the rojection of the total electron in along z m z =,1. Each tate i further characterized by the hole-in direction, leading to the ix level dilayed, four of which are otically active. At zero magnetic field, + light only coule to T and to T, with diole moment of / 2 and, reectively. Since the electron Zeeman energy 5 ev i ignificantly maller than eh, the Voigt magnetic field ha little effect on thee tate. They do become omewhat mixed, allowing a mall diole moment for the to T + tranition with + light. Since the otical ule have a bandwidth of 1 mev, any one of thee trilet tate can be excited for ule in thi hoton energy range. Summing over each tranition hould give a net olarization due to the larger diole for T. The inglet -hell trion S tate i exected to be higher in energy by everal mev due to ee. 29,3 For + ule, the to S tranition i allowed with a diole moment of / 2. Figure 6a lot the calculated in olarization due to thee trilet and inglet -hell trion a a function of the excitation energy relative to S for a ingle QD. The tate i hown a a oitive in olarization for eaier comarion to exerimental data. The trilet tate give a net negative ignal and the inglet tate give a oitive ignal of equal amlitude. Note that the linewidth of the feature i exected to be largely determined by the ule bandwidth intead of the trion linewidth. The QD are modeled by aniotroic 2D harmonic otential. The electron and hole are decribed by Fock-Darwin tate harmonic ocillator with lateral ize a x and a y in thi otential. We chooe a Gauian ditribution of ize with central ize that give the - litting in the exeriment. Thee geometric arameter determine all electronelectron and electron-hole Coulomb and exchange integral. The analytical wave function allow u to derive imle caling relation between the Coulomb and exchange integral in the excited tate and thoe in the hell. A tyical -hell electron-hole exchange energy, eh i known from exeriment and theory to be in the range 5 1 ev. 31 Uing thee value in our model we obtain eh in the hell conitent with exerimental value of 2 ev. 15 Alo, the

5 ELECTRON SPIN POLARIZATION AND DETECTION IN average ee in the hell derived in our model i conitent with tyical exerimental value of everal millielectron volt. 29 The effect of inhomogeneity are included in Fig. 6b for an enemble of QD. Only QD with an S energy near the robe hoton energy are ued for calculating the in olarization imilar to exeriment. Thi inhomogeneou ditribution broaden the feature in Fig. 6a but the negative di and oitive eak are till quite aarent. Deite the inhomogeneou broadening, the in electivity, defined a n w,n w,n / n w,n +w,n, i till high for mot of thee feature. The electivity normalize the average in olarization by the total abortion robability, uch that a in electivity of 1 or 1 indicate that only in-u or indown electron, reectively, are excited to trion tate. The in electivity i 1 for the -hell and -hell inglet feature at and 3 mev in Fig. 6b, reectively, ince thee trion have clear in-election rule and are ectrally earated from other trion tate. The in electivity i only about 1/3 for the -hell trilet feature at 22 mev ince there are three cloely aced tate with different in-election rule. Comaring the calculated in olarization in Fig. 6b to the elliticity in Fig. 3b give ome qualitative agreement between exeriment and theory but in exeriment there i clearly no negative di. There are everal oibilitie for why thi di doe not occur. Firt, if the diole moment for T and T are cloer to equal intead of differing by 2, the T contribution will vanih, leaving only the S contribution. Second, it i oible that the aumtion that recombination doe not affect the in olarization i faulty, leading PHYSICAL REVIEW B 81, to differing degree of in olarization deending on the trion dynamic. One might alo wonder if the tranition hel exlain the feature at 3 mev but we do not find that thee tate account for the difference. Exeriment in ingle QD, where the different tranition can be identified more eaily may hel reolve thi dicreancy. IV. CONCLUSIONS We have erformed two-color time-reolved ectrocoy of in dynamic in an enemble of InA QD. When the robe i centered on -hell trion, a trong ignal from receing electron in i oberved when uming near the robe and about 3 mev above, conitent with -hell trion. A imilar reonance i oberved when the um and robe hoton energie are revered. Thee reult indicate that electron in can be directly olarized and detected uing -hell trion. Thi effect i oible due to the exchange litting of trilet and inglet -hell trion, which are exected to olarize electron in in ooite direction. Uing the -hell trion for in maniulation may be ueful for controlling the atial extent of the carrier wave function and for earating the wavelength of otical control ule from the QD emiion wavelength. ACKNOWLEDGMENTS We thank T. L. Reinecke and Sohia E. Economou for helful uggetion on the manucrit. Thi work i uorted by the U.S. Office of Naval Reearch. 1 X. Xu, Y. Wu, B. Sun, Q. Huang, J. Cheng, D. G. Steel, A. S. 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