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Wuhan University Journal

Characteristics of Quantum Beat of Degenerated Four-Wave Mixing in In_xGa_(1-x)N/GaN Quantum Well

Guiguang Xiong

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

Based on the quasi-classical theory on the interaction of laser and matter,the characteristics of heavy and light-hole quantum beat of degenerated four-wave mixing in In_xGa_(1-x)N/GaN quantum well have been analyzed by solving the Bloch equations. The model used for describing the phenomena can be considered as a three-level system consisting of the ground state and two excited states from which the wave packet is formed and the model is a Λ-type system. It is shown that the intensity of the oscillation detected in degenerated four-wave mixing is modulated with real time and has the typical characteristics of quantum beat. The period of the beat increase with the increase of In content (x).When x=0.125,the period is 120 fs and when x=0.25,the period is 180 fs.The intensity and the amplitude of the oscillation of the sighal have great dependence on the dephasing rate of the quentum well and increase with the derease of the dephasing rate.

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Based on the quasi-classical theory on the interaction of laser and matter,the characteristics of heavy and light-hole quantum beat of degenerated four-wave mixing in In_xGa_(1-x)N/GaN quantum well have been analyzed by solving the Bloch equations. The model used for describing the phenomena can be considered as a three-level system consisting of the ground state and two excited states from which the wave packet is formed and the model is a Λ-type system. It is shown that the intensity of the oscillation detected in degenerated four-wave mixing is modulated with real time and has the typical characteristics of quantum beat. The period of the beat increase with the increase of In content (x).When x=0.125,the period is 120 fs and when x=0.25,the period is 180 fs.The intensity and the amplitude of the oscillation of the sighal have great dependence on the dephasing rate of the quentum well and increase with the derease of the dephasing rate.
Summary form only given. Here, we use the polarization selection rules for four-wave mixing (FWM) and a test that was originally designed to distinguish between quantum beats and polarization interference to demonstrate the presence of strong exciton-exciton correlations in GaAs-AlGaAs multiple quantum wells. We show that when the four-wave-mixing signal is produced by two pulses having the same circular polarizations that quantum-beat-like behavior is observed. The latter observation is contrary to the predictions based on either the density matrix equations for two independent three-level systems (without many body effects) or the conventional semiconductor Bloch equations (SBE), both of which predict that polarization interference, but not quantum beats, should be observed. Consequently, these observations provide clear evidence for exciton-exciton correlations and evidence that those correlations go beyond those contained in the SBE. The procedure described here provides a simple effective test for such processes. Finally, we show that the quantum-beating-like behavior can be reproduced by including a density-dependent dephasing term (so-called excitation-induced dephasing, or EID) in the density matrix equations.
We describe a novel three-pulse degenerate four-wave mixing configuration that permits the direct observation of the coherence between the σ+ and the σ− exciton states in a GaAs quantum well excited in a two-photon process. It is found that the phase coherence between the two single heavy-hole exciton states decays with a time constant that is considerably longer than the dephasing time of the coherence between these states and the ground state (interband coherence). All the experimental data are well described by numerical solutions of the optical Bloch equations for a phenomenological multilevel model.
Shifts in the relative phases of quantum beats in the time-resolved four-wave-mixing signals from a GaAs/Alx{\mathrm{Al}}_{\mathit{x}}Alx​${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As multiple quantum well are observed. The relative phases are shown to depend strongly on the intensities of the incident pulses as well as their detuning from the heavy-hole exciton. A simple coupled six-level model shows that the phases of the quantum beats are directly determined by many-body effects such as density-dependent dephasing and the local-field correction.
The nature of the beat modulations observed in nonlinear four-wave mixing in semiconductors is determined by spectral resolution of the time-integrated four-wave-mixing signals. Beats between close-lying bound-exciton resonances in CdSe are found to be described by macroscopic polarization interferences between two noninteracting two-level systems. Beats between heavy-hole excitons and light-hole excitons in GaAs quantum wells, on the other hand, are described by a three-level system, i.e., as a true quantum interference phenomenon.
We have investigated, by fully-time-resolved degenerate four-wave mixing (FWM), excitonic coherence phenomena in single GaAs∕AlGaAs\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}GaAs∕AlGaAs quantum wells which are known to exhibit localization. A magnetic field (0−−12T)(0--12\phantom{\rule{0.3em}{0ex}}\mathrm{T})(0−−12T) was applied in Faraday geometry as a means of altering the nature of the excitonic transitions in a controlled manner. When the system is excited by a sequence of pulses tuned in resonance with the heavy-hole excitons, the predominant behavior observed at positive interpulse delays is beating in the FWM emission due to polarization interference between uncoupled excitons localized by monolayer islands. For negative interpulse delay the variation of beat phase with delay changes sign as the magnetic field is increased. In order to understand this feature, we modeled a coupled three-level system and included local field effects as a simple phenomenological approach to describing many-body terms. Comparison with experiments shows that with a larger magnetic field, the contribution to the signal from the coupled system reduces while that from two noninteracting two-level systems increases. We attribute this to the increased confinement of the excitons with field, leading to reduced wavefunction overlap, and hence reduced coupling.
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.