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CRC Press eBooks

Coherent exciton dynamics : time-resolved polarimetry

Arthur L. Smirl

Published Dec 5, 2020• 0 citations
Publisher

Abstract

The studies described in this chapter convince the reader that time-resolved polarimetry is an extremely sensitive way to study many body effects. The vectorial dynamics contain useful information about many-body effects, quantum interference and optical anisotropies that would be difficult to obtain in any other way. The chapter begins with a brief review of some of the four-wave-mixing (FWM) techniques that have been most commonly used to measure the coherent emission from multiple quantum wells (MQWs). The ellipticity and the fraction of unpolarised light are both significantly smaller for the negative delay. These features provide additional tests for any proposed model that purports to describe coherent excitonic dynamics in MQWs. The chapter discusses the treatment of excitons in semiconductors as two-level systems, and follows with a detailed review of the solutions to the density matrix equations for two independent two-level systems, with an emphasis on the vectorial nature of the FWM emission from such systems.

DOI
10.1201/9781003072829-2

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The studies described in this chapter convince the reader that time-resolved polarimetry is an extremely sensitive way to study many body effects. The vectorial dynamics contain useful information about many-body effects, quantum interference and optical anisotropies that would be difficult to obtain in any other way. The chapter begins with a brief review of some of the four-wave-mixing (FWM) techniques that have been most commonly used to measure the coherent emission from multiple quantum wells (MQWs). The ellipticity and the fraction of unpolarised light are both significantly smaller for the negative delay. These features provide additional tests for any proposed model that purports to describe coherent excitonic dynamics in MQWs. The chapter discusses the treatment of excitons in semiconductors as two-level systems, and follows with a detailed review of the solutions to the density matrix equations for two independent two-level systems, with an emphasis on the vectorial nature of the FWM emission from such systems.
A dual-channel version of spectral interferometry is used to completely characterize the extremely weak ultrashort coherent four wave mixing (FWM) emission from multiple quantum wells (MQWs) by time resolving the polarization state, as well as the scalar amplitude and phase. The amplitudes and the phases of the x and y components of the coherent FWM emission are found to exhibit systematic (but distinct) variations with excitation fluence, time delay between the two incident pulses, detuning of the laser wavelength from the heavy hole (hh) exciton, and the orientation of the input polarizations. From these, a self consistent picture of the temporal dynamics of the amplitude, phase and polarization state is obtained that delineates the roles of many body effects, such as local field corrections, excitation-induced dephasing and biexcitons, in determining the excitonic dynamics.
Coherent emission process of excitons in a layered compound GaSe， and in ZnSe/ZnSo．isSeo．s2 multiple quantum wells has been directly observed for the first time， by means of two independent newly-developed methods； time-resolved Brewster-angle reflectance （TRBR） spectroscopy and time-resolved four-wave-mixing （TRFWM） spectroscopy． In TRBR measurement， we have succeeded in observing a distinct free-induction-decay of coherently-driven polarization， with an oscillatory behavior due to finely split exciton levels． An analysis on the basis of a s imple model provides key information on the dynamical phase relaxation process． The result of the TRFWM measurement gives the comprehensive treatment of two dephasing processes； destructive interference due to static inhomogeneous broadening， and dynamical homogeneous phase relaxation． An analysis of TRFWM intensity enables one to exactly determine the homogeneous phase relaxation time． Finally， we show that a comparison between the coherent emission signal measured by TRBR or TRFWM， and third-order nonlinear correlation profile observed by time integrated FWM measurement enables one to make distinction between which of quantum - or classical interference effect causes the beat feature seen in the coherent emission signal．
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.
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.
The coherent emission from excitons corresponding to different subband transitions in a 500 Åbroad GaAs/AlGaAs quantum well is studied by spectrally resolved transient four-wave mixing (FWM). For the simultaneous excitation of several subband transitions, the dephasing times of the lowest exciton and higher- order exciton transitions are determined from the width of the resonances in the FWM spectrum. The decay of the spectrally integrated FWM signal as a function of the time delay between the excitation laser pulses does not reflect the dephasing times but is determined by the laser pulse width for multi-subband excitation. This is indicative of quantum interference between exciton and continuum transitions. Many-body Coulomb effects have to be included in a theoretical treatment of these experimental observations.