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Influence of exciton–exciton interaction and disorder on optical dephasing of 2-D excitons

J. Kühl, E. J. Mayer, Charlie Smith, D. Bennhardt, P. Thomas, Kimberly Bott, O. Heller, Steven T. Cundiff

Published May 8, 1994• 0 citations
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Abstract

Time-integrated (TI) and time-resolved (TR) degenerate-four-wave-mixing (DFWM) experiments performed on the exciton transition in GaAs quantum wells (QW) have shown strong variations of the signal features with the polarization configuration of the two excitation pulses that cannot be explained in the frame of the model describing the 2-D excitan by two noninteracting twofold-degenerate three-level systems with circular dipole transition rules.1

Related papers

Influence of exciton-exciton interactions on the coherent optical response in GaAs quantum wells

K. Bott, O. Heller, D. Bennhardt +7 more

The degenerate-four-wave-mixing response of excitons in GaAs quantum wells is modeled using the optical Bloch equations including exciton-exciton interactions. The results display a strong dependence on the polarization of the excitation pulses. The model predicts intensity and polarization dependences of the time-integrated signal and characteristic temporal features of the time-resolved and time-integrated response in excellent agreement with observations.

Physical review. B, Condensed matter•Dec 15, 1993•192 citations

Theory for polarization-dependent four-wave-mixing signals in quantum wells

D. Bennhardt, T. Meier, P. Thomas +3 more

In degenerate four-wave-mixing (DFWM) experiments the polarization of the incident laser pulses can have a strong influence on the measured signal. For GaAs quantum wells a number of DFWM experiments were performed by using either parallel or perpendicular polarization of the incident laser pulses. Experimentally, it turned out that some characteristic features of the signal differ appreciably for the two configurations. In particular, different dephasing times, phase shifts of the quantum beats, different time-resolved behavior (echoes versus free-induction decay), and intensity dependence of the measured signal have been reported.1–3

Quantum Electronics and Laser Science Conference•May 2, 1993•0 citations

Polarization selection rules for degenerate four-wave mixing on 2D excitons

J. Kühl, Richard Eccleston, E. J. Mayer +2 more

Several recent two-pulse degenerate four- wave-mixmg experiments on 2D excitons in GaAs showed considerably faster dephasing rates for cross-polarized beams than for colinear polarization.1,2 Moreover, time-resolved analysis of the DFWM signal on some samples revealed a photon echo and a free-induction decaylike behavior for the parallel and perpendicular polarizations, respectively.1

Quantum Electronics and Laser Science Conference•May 2, 1993•0 citations

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

Bipul Pal, Arvind S. Vengurlekar

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.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jun 13, 2002•0 citations

Excitation-Induced Phase Shifts of Heavy and Light Hole Quantum Beats in Multiple Quantum Wells

Wei E. I. Sha, A. E. Paul, Shekhar Patkar +1 more

In recent years, transient four-wave mixing (FWM) techniques have been used to investigate the dephasing times of non-equilibrium carriers in semiconductor heterostructures by monitoring the decay of the macroscopic polarization. Initially, this decay was measured by temporally-integrating the scattered FWM signal as a function of time delay between two (or more) pump pulses. More recently, the macroscopic polarization decay has been measured by time-resolving the FWM signal by cross correlating it with an ultrashort laser pulse via frequency up-conversion in a nonlinear crystal. When excitons with slightly different energies are excited, oscillations (or beats) have been observed both in the time-integrated FWM signal and in the time-resolved FWM signal. Such beats have been observed, for example, between light- and heavy-hole excitons and between excitons in wells of different widths. Both the spectral behavior1 of the time-integrated FWM signal and the temporal behavior2 of the time-resolved signal have been shown to allow the distinction between the polarization interference associated with two independent oscillators and the quantum beats associated with two coupled oscillators which share a common level. In addition, it has been demonstrated3 that the quantum beats produced by incident pulses with parallel polarizations are exactly out of phase (by π) with the beats produced by orthogonally polarized pulses. In each case1-3, the period and phase of the beats and the polarization of FWM signal were explained by using a six-level model, which excluded many-body effects, to describe the J=1/2 conduction and J=3/2 valence states. Within the last few months, however, it has been shown that a complete description of the polarization selection rules for the FWM signal requires excitation-induced dephasing4 or disorder-induced coupling of the σ + and σ – excitonic transitions5.

International Conference on Ultrafast Phenomena•Jan 1, 1994•0 citations

Line shape of time-resolved four-wave mixing

Martin Wegener, D. S. Chemla, Stefan Schmitt-Rink +1 more

Time-resolved four-wave-mixing experiments are usually interpreted in terms of noninteracting two-level systems in order to obtain information on the polarization dephasing time ${\mathit{T}}_{2}$. Recent experiments involving excitonic resonances in semiconductor quantum wells (including results presented in this paper) show striking qualitative deviations from this simple picture. In particular, an exponential tail is observed at low excitation for negative time delays. At high excitation, the four-wave-mixing signal is found to evolve into two distinct temporal maxima. We demonstrate that the microscopic origin of this time dependence can be understood in terms of coherent exciton-exciton interactions. We show in fact that this behavior is more general and should be seen in numerous dense media where strong nonlinear interactions of polarizations occur. In addition to presenting rigorous numerical results, we analyze two simple situations in which such interactions exist: dielectric media with local-field effects and the anharmonic oscillator. We derive analytical expressions for their time-dependent four-wave-mixing response and discuss the physical origin of these new nonlinear-optical effects.

Physical Review A•Nov 1, 1990•376 citations
Time-integrated (TI) and time-resolved (TR) degenerate-four-wave-mixing (DFWM) experiments performed on the exciton transition in GaAs quantum wells (QW) have shown strong variations of the signal features with the polarization configuration of the two excitation pulses that cannot be explained in the frame of the model describing the 2-D excitan by two noninteracting twofold-degenerate three-level systems with circular dipole transition rules.1
In degenerate four-wave-mixing (DFWM) experiments the polarization of the incident laser pulses can have a strong influence on the measured signal. For GaAs quantum wells a number of DFWM experiments were performed by using either parallel or perpendicular polarization of the incident laser pulses. Experimentally, it turned out that some characteristic features of the signal differ appreciably for the two configurations. In particular, different dephasing times, phase shifts of the quantum beats, different time-resolved behavior (echoes versus free-induction decay), and intensity dependence of the measured signal have been reported.1–3
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.
In recent years, transient four-wave mixing (FWM) techniques have been used to investigate the dephasing times of non-equilibrium carriers in semiconductor heterostructures by monitoring the decay of the macroscopic polarization. Initially, this decay was measured by temporally-integrating the scattered FWM signal as a function of time delay between two (or more) pump pulses. More recently, the macroscopic polarization decay has been measured by time-resolving the FWM signal by cross correlating it with an ultrashort laser pulse via frequency up-conversion in a nonlinear crystal. When excitons with slightly different energies are excited, oscillations (or beats) have been observed both in the time-integrated FWM signal and in the time-resolved FWM signal. Such beats have been observed, for example, between light- and heavy-hole excitons and between excitons in wells of different widths. Both the spectral behavior1 of the time-integrated FWM signal and the temporal behavior2 of the time-resolved signal have been shown to allow the distinction between the polarization interference associated with two independent oscillators and the quantum beats associated with two coupled oscillators which share a common level. In addition, it has been demonstrated3 that the quantum beats produced by incident pulses with parallel polarizations are exactly out of phase (by π) with the beats produced by orthogonally polarized pulses. In each case1-3, the period and phase of the beats and the polarization of FWM signal were explained by using a six-level model, which excluded many-body effects, to describe the J=1/2 conduction and J=3/2 valence states. Within the last few months, however, it has been shown that a complete description of the polarization selection rules for the FWM signal requires excitation-induced dephasing4 or disorder-induced coupling of the σ + and σ – excitonic transitions5.
Time-resolved four-wave-mixing experiments are usually interpreted in terms of noninteracting two-level systems in order to obtain information on the polarization dephasing time T2{\mathit{T}}_{2}T2​. Recent experiments involving excitonic resonances in semiconductor quantum wells (including results presented in this paper) show striking qualitative deviations from this simple picture. In particular, an exponential tail is observed at low excitation for negative time delays. At high excitation, the four-wave-mixing signal is found to evolve into two distinct temporal maxima. We demonstrate that the microscopic origin of this time dependence can be understood in terms of coherent exciton-exciton interactions. We show in fact that this behavior is more general and should be seen in numerous dense media where strong nonlinear interactions of polarizations occur. In addition to presenting rigorous numerical results, we analyze two simple situations in which such interactions exist: dielectric media with local-field effects and the anharmonic oscillator. We derive analytical expressions for their time-dependent four-wave-mixing response and discuss the physical origin of these new nonlinear-optical effects.