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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Exciton coherence in GaAs quantum wells probed by four wave mixing measurements at high excitation intensities

Bipul Pal, Arvind S. Vengurlekar

Published Jun 13, 2002• 0 citations
Publisher

Abstract

We perform two beam time integrated (TI) degenerate four wave mixing (DFWM) measurements on 8~nm GaAs quantum wells (QW). Pulses from a Ti-Sapphire laser resonantly excite only 1s heavy hole excitons. The power density of the leading pulse (I1) is increased, keeping that of the delayed pulse fixed and relatively small. We measure the TI-DFWM signal at different delays as well as the DFWM spectra at a fixed delay, as I1 is increased. We find that the dephasing rate, after an initial increase with I1, becomes independent of I1 for large I1. The spectrally integrated DFWM signal, which probes the coherent polarization of the resonantly excited QWs, initially increases with I1, reaches a peak and then decreases as 1/(root)I1 at large I1. The results are compared with theoretical models of exciton coherence.

DOI
10.1117/12.470412

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We perform two beam time integrated (TI) degenerate four wave mixing (DFWM) measurements on 8~nm GaAs quantum wells (QW). Pulses from a Ti-Sapphire laser resonantly excite only 1s heavy hole excitons. The power density of the leading pulse (I1) is increased, keeping that of the delayed pulse fixed and relatively small. We measure the TI-DFWM signal at different delays as well as the DFWM spectra at a fixed delay, as I1 is increased. We find that the dephasing rate, after an initial increase with I1, becomes independent of I1 for large I1. The spectrally integrated DFWM signal, which probes the coherent polarization of the resonantly excited QWs, initially increases with I1, reaches a peak and then decreases as 1/(root)I1 at large I1. The results are compared with theoretical models of exciton coherence.
We study the coherent response of an optically dense exciton system in GaAs quantum wells (QWs). For this, we resonantly excite 1s1s1s heavy-hole excitons in the QWs at 8 K with subpicosecond laser pulses. The excitonic polarization is probed using time integrated (TI) degenerate four wave mixing (DFWM) measurements in self-diffraction geometry. The average power density (I1){(I}_{1})(I1​) of the leading laser pulse is systematically increased to large values, keeping that of the delayed pulse small and fixed. The dephasing rate of the excitonic coherent polarization (determined by the rate of decrease of the TI-DFWM signal with delay between the exciting pulses) attains saturation at large I1{I}_{1}I1​ after an initial rise at small I1.{I}_{1}.I1​. In comparison, the coherent polarization (as given by the DFWM signal at a fixed delay) increases initially with I1,{I}_{1},I1​, reaches a peak and then decreases at large I1.{I}_{1}.I1​.
We study exciton dephasing in 8 nm GaAs quantum wells (QW) at 8 K by resonantly exciting the excitons at low densities. For this, we perform femtosecond degenerate four-wave mixing (DFWM) measurements using two laser beams. The excitons in the QWs are inhomogeneously broadened, with a photoluminescence linewidth of 1.8 meV. We investigate how the time integrated DFWM signal and its decay rate $\ensuremath{\eta}$ change as the average intensity of either of the two exciting beams is varied separately. We find that the dependence of $\ensuremath{\eta}$ on the intensity of the first pulse is about twice as that for the delayed pulse. We compare the results with a theory based on optical Bloch equations and relaxation rate approximation, accounting phenomenologically for dephasing due to exciton-exciton scattering.
Three-beam time-integrated transient four-wave mixing (TFWM) is used to probe both light-hole (LH) and heavy-hole (HH) exciton coherences in weakly disordered GaAs quantum wells. The period of the quantum beats between the LH and the HH exciton coherences changes as a function of first-second pulse delay. A theoretical model for the TFWM signal, including exciton dephasing rates that vary with frequency across the inhomogeneous linewidth, reproduces the observations. The inclusion of inhomogeneous dephasing also improves the correspondence between theory and experiment when data as a function of both first-second and second-third pulse delays are simultaneously examined.
We resonantly excite the n=2 excitons at 8 K in 13 nm and 17.5 nm GaAs quantum wells using 0.5 ps pulses from a Ti-Sapphire laser and perform four wave mixing (FWM) measurements. The exciton dephasing time is deduced by fitting the FWM spectra to a numerical solution of the optical Bloch equations for the excitonic resonance. The finite pulse width and presence of small inhomogeneous broadening are taken into account. The homogeneous linewidth thus obtained at different low excitation intensities has a linear dependence on the intensity. The zero intensity intercept is essentially governed by the n=2 exciton lifetime due to intersubband relaxation, the pure transverse dephasing contribution being relatively less important. We deduce the exciton lifetime to be 0.9 ps and 2.6 ps for the 13 nm and 17.5 nm QWs, respectively.
Spectrally resolved and time-integrated degenerate four-wave mixing (FWM) experiments with ultra-short pulses have been used to investigate the relaxation times and coherent interactions of excitons in the Boltzmann and in the quantum kinetic regime in ZnSe single quantum wells.Three-pulse FWM experiments using 100 fs pulses in a 10 nm thick ZnSe/ZnMgSe single quantum well reveal nearly equal zero-density dephasing rates for coherences between + σ and - σ heavy-and/or light-hole exciton states as compared to the dephasing rate of the interband coherence between these states and the ground state.The measurements also demonstrate that exciton-exciton scattering destroys the phase coherence between heavy-and light-hole excitons about three times more effectively than the coherence between + σ and + σ heavy-hole excitons.The different coherent nonlinear signals obtained in a three-beam FWM experiment are explained and reproduced by numerical calculations of the optical Bloch equations for a ten-level model including excitation induced dephasing (EID).Two-beam FWM experiments using 30 fs pulses on a 10 nm ZnSe quantum well reveal marked quantum beats and a pronounced non-exponential decay for delay times smaller ~500 fs.The pronounced peak at pulse overlap is attributed to rapid destructive interference of the created polarization and to spin dependent quantum kinetic effects caused by the transient formation of an electron-hole (eh) pair grating.The three-beam FWM trace shows a bi-exponential decay which is attributed to a nonlinear polarization that is caused by the interaction of polarization 3 k with both an exciton grating and an eh-pair grating.Model calculations using the OBEs of a two level system that includes ∑ -+
We investigate the spectral properties of the excitonic nonlinear response in a GaAs quantum-well sample containing wells of different thicknesses. We observe both the heavy-hole biexciton and the light-hole biexciton in the transient four-wave mixing spectrum and estimate their binding energy dependence on well width. For moderate excitation densities the signal for negative delay at the heavy-hole exciton and biexciton resonances is due to two-photon transitions to the biexciton states through the exciton states. The temporal behavior of the transient four-wave mixing signal from the heavy-hole exciton resonance is strongly dependent on the spectral position of the laser. We show that this effect is due to interference phenomena and to excitation-induced dephasing.