Preservation of quantum coherence after exciton-exciton interaction in quantum wells N. Garro, 1,2 S. P. Kennedy, 1 R. T. Phillips, 1 G. Aichmayr, 3, * U. Ro ¨ ssler, 3,² and L. Vin ˜ a 3 1 Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, United Kingdom 2 Institut de Cie `ncia dels Materials, Universitat de Vale `ncia, E-46071 Vale `ncia, Spain 3 Departamento Fı ´sica de Materiales, Universidad Auto ´noma Madrid, E-28049 Madrid, Spain Received 14 October 2002; revised manuscript received 9 January 2003; published 17 March 2003 The dynamics of exciton-exciton interaction in quantum wells has been investigated by monitoring the time-resolved resonant secondary emission that follows excitation with linearly and circularly polarized light. Preservation of quantum beating in the cross-polarized emission demonstrates that spin relaxation can take place, for some scattering channels, without total quantum coherence loss. Interexciton electron exchange is the scattering mechanism that explains the persistence of the beating and, since it is sensitive to the fine structure of excitons, the shift by  in the phase of the beating observed in the experiment. DOI: 10.1103/PhysRevB.67.1213XX PACS numbers: 78.47.+p, 71.70.Gm, 78.66.Fd Optical properties of low-dimensional semiconductor sys- tems and devices depend strongly on the excitation density ( n X ). For n X below 3 10 11 cm -2 and at low temperatures, excitons are stable and dominate the optical response of GaAs quantum wells QW’s near the absorption edge. Within this regime of moderate excitation density ( n X 10 9 cm -2 ) exciton-exciton scattering plays a major role in the resonant response of QW’s and, as the dominating phase- breaking mechanism, governs the dynamics of coherent tran- sients. Since excitons confined in low-dimensional semicon- ductor systems have been suggested as possible candidates for quantum computation 1 it is important to understand the mechanisms involved in the loss of optical coherence be- tween the excitonic ensemble and the exciting light. The study of exciton dephasing has been most often attempted by means of nonlinear techniques. 2 Nevertheless, coherent fea- tures are also present in the linear response of QW’s: the resonant secondary nonspecular emission RSE has a co- herent component resulting from scattering with static disorder. 3 Thus time-resolved RSE can be used as a probe of the coherence of the excitonic ensemble providing informa- tion about scattering with dynamic disorder, such as exciton- exciton scattering, that leads to exciton dephasing. 4,5 Recent studies have shown that exciton-exciton interaction also con- tributes to the depolarization of RSE due to exciton spin relaxation. 6,7 The efficiency of such spin-relaxation channels increases with increasing excitation ellipticity. In the limiting case of linearly polarized excitation, the degree of polariza- tion of RSE decays in a time scale comparable to typical dephasing times for GaAs QW’s 10 ps and depends strongly on n X . These experimental results are well ex- plained in terms of interexciton exchange of carriers. 8,9 For circularly polarized excitation, on the other hand, spin relax- ation is a much slower density-independent process. 10,11 Periodic oscillations can appear in the time evolution of RSE due to the simultaneous resonant excitation of more than one excitonic transition. Beating between heavy-hole hh and light-hole lh excitons has been observed in the emission of wide QW’s. 12,13 The visibility of the beating de- cays in a time scale of the order of 10 ps and depends on n X . Determining the origin of the beating—whether it results from the quantum nature of the superposition of states or from classical interferences at the detector—is not trivial. Distinguishing between these two possibilities required per- forming a specific experiment in the case of beating observed in time-resolved four-wave mixing. 14 So far there are no con- clusive studies about the nature of the beating present in the linear emission of QW’s. In this Rapid Communication we address two important issues regarding exciton coherence in QW’s: the nature of hh-lh exciton beating in RSE and the effect of exciton- exciton interaction as a coherence-breaking mechanism. We studied the depolarization of time-resolved RSE from wide QW transitions after excitation with linearly polarized light in the density regime where exciton-exciton scattering is the dominant spin-relaxation mechanism. The improved time resolution of our experiment allowed the observation of sev- eral features indicating that spin relaxation can take place without coherence loss. We have identified the exciton- exciton scattering mechanism responsible for such effects. The experimental results presented in this Rapid Commu- nication correspond to a single 15-nm GaAs QW with Al 0.33 Ga 0.67 As barriers sample A ) and a multiple-QW struc- ture containing ten repetitions of 20-nm GaAs wells sepa- rated by GaAs/AlAs superlattice barriers sample B ). Both samples showed narrow emission linewidths at low tempera- tures, with full width at half maximum of 0.8 meV and 0.7 meV for samples A and B, respectively. We measured the time evolution of the RSE by means of two-color up- conversion spectroscopy for more details about the experi- mental setup see Ref. 13. Excitation and gating pulses were 140-fs long 13-meV bandwidth, which kept the time reso- lution below 200 fs, shorter than in previous studies. 6,7 Excitation of the sample was done in the backscattering ge- ometry with the laser pulse propagating parallel to the growth direction z of the sample. All measurements were done at 6 K. Time-resolved RSE spectra of sample A for identical n X but corresponding to different excitation and detection con- ditions are plotted in Fig. 1. The excitation pulse was either circularly polarized a or linearly polarized along the x di- rection b and the detected emission was copolarized solid lines and cross-polarized dashed lines with respect to the excitation. Copolarized emission has an intense spike at t RAPID COMMUNICATIONS PHYSICAL REVIEW B 67, 121302R2003 0163-1829/2003/6712/1213024/$20.00 ©2003 The American Physical Society 67 121302-1