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Journal of the Optical Society of America B

Polarization-state beating in four-wave-mixing experiments on ZnSe epilayers

A. Tookey, D. J. Bain, Ian J. Blewett, Ian Galbraith, Ajoy Kumar Kar, Brian S. Wherrett, B. Vögele, Kevin A Prior, Brian C. Cavenett

Published Jan 1, 1998• 8 citations
Publisher

Abstract

The polarization angle of the time-integrated four-wave-mixing signal from a ZnSe epilayer is found to oscillate as a function of the delay time between the two incident pulses, the modulation depth being dependent on the polarization angle between the incident pulses. The oscillation is shown to be a feature of heavy-hole–light-hole quantum beating, and is described by a solution of the optical Bloch equations.

DOI
10.1364/josab.15.000064

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The polarization angle of the time-integrated four-wave-mixing signal from a ZnSe epilayer is found to oscillate as a function of the delay time between the two incident pulses, the modulation depth being dependent on the polarization angle between the incident pulses. The oscillation is shown to be a feature of heavy-hole–light-hole quantum beating, and is described by a solution of the optical Bloch equations.
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 complex polarization behavior of quantum beating between heavy- and light-hole excitons in nonlinear pump-and-probe spectroscopy is experimentally investigated. The strain-split free excitons in thin high-quality ZnSe layers embedded in ternary ZnSx{\mathrm{ZnS}}_{\mathit{x}}ZnSx​${\mathrm{Se}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$ barriers served as the three-level system involved. Spectrally integrated pump-and-probe experiments confirm the theoretically predicted dependence of the quantum-beat phase on the relative polarization of the exciting fields. These observations are discussed in comparison with results from four-wave mixing obtained when using the same experimental setup. Beyond that, spectrally resolved transients measured on the light-hole resonance exhibit pronounced, weakly damped beating phenomena even at negative delay, i.e., with the probe pulses preceding the pump pulses. Additionally, for cross-polarized beams the quantum-beat phase is strongly dependent on the energy of detection. It turns out that the phase observed in the spectrally integrated mode is determined by the off-resonant contributions. \textcopyright{} 1996 The American Physical Society.
We report on the study of quantum beats in the time-integrated four-wave mixing signal in reflection geometry from a pair of excitons with different valence orbitals in GaN and ZnSe. We observe a \ensuremath{\pi}-phase shift between quantum beats in the co- and cross-linear polarization configuration, and nearly 100% modulation of the signal for both materials. In the co-circular polarization configuration, the observed phases of the quantum beats at the frequency of the A exciton in GaN and heavy-hole exciton in ZnSe are 0.2\ensuremath{\pi} and 0.1\ensuremath{\pi}, respectively. The phases of the quantum beats change sign for co- and counter-circular polarization configurations and also for A- (heavy-hole) and B-(light-hole) excitons in GaN(ZnSe). We describe the third-order coherent optical response of the exciton pair with different valence orbitals by taking into account the finite memory depth of the four-particle correlation. In particular, our experimental findings indicate that excitons with different valence orbitals and equal angular momentum attract each other similar to excitons with the same valence orbitals but opposite angular momentum. Excitons with different orbitals and opposite angular momenta repel one another. The comparison between experimental and theoretical results allows us to develop a quantitative analysis of the four-particle correlation in the presence of an exciton pair with different valence orbitals. We show that the observed \ensuremath{\pi}-phase shift and nearly 100% modulation of the signal in the co- and cross-linear polarization configuration impose restraints on the memory functions, which describe the exciton-exciton interaction. These restraints imply, in particular, that electron spins play a more important role in the exciton-exciton interaction in comparison to hole spins. We show that a striking similarity, which we observe in the quantum beat signal from GaN and ZnSe, originates from the strong four-particle correlation contribution to the third-order excitonic nonlinearity.
Recent transient four-wave-mixing experiments in the two-pulse photon-echo configuration performed on GaAs quantum wells have yielded the surprising result that in some samples the T2{\mathit{T}}_{2}T2​ time obtained from the polarization decay can be shorter for cross-polarized input fields than for parallel input fields. A concomitant change from photon-echo to free-induction-decay behavior has also been observed. A phenomenological model is presented which explains these observations by means of a disorder-induced coupling of the ${\mathrm{\ensuremath{\sigma}}}^{+}$ and ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{-}}}$ exciton transitions which is inhomogeneous in coupling strength. Such coupling also leads to a remarkable change in the light-hole--heavy-hole exciton quantum beat phase as a function of pulse delay for a critical relative orientation of the polarization of the incident pulses. Experimental observations of this effect are presented to support the validity of the model.
The contribution of bound excitons and biexcitons to degenerate four-wave mixing signals is investigated in high-quality biaxially strained ZnSe layers. For the former complexes signatures of polarization interference with free excitons are found in time-resolved four-wave mixing, whereas spectrally resolved data point to the occurrence of quantum beating. Thus this system behaves as a mixture of independent two-level systems on the one hand and three-level systems on the other. Biexcitons contribute to the signal mainly at negative delay between the exciting pulses and are identified by means of spectrally resolved measurements and by use of different configurations of the pulse polarization. Complete agreement is found between the selection rules for biexcitons (and excitons) and the experimental data.
We report interferometric four-wave-mixing (FWM) experiments on ZnSe quantum-well (QW) structures. By varying the phase relation of two phase-locked pulses in direction k1 (interferometric pulses) and using an additional pulse with wave vector k2 we observe an oscillating FWM signal in the direction 2 k2 — k1. This technique is specially suitable to investigate the influence of effects beyond third order with respect to the optical field, since these effects manifest themselves as higher integer harmonics in the observed FWM trace. We found a maximum influence of higher harmonics for overlapping interferometric pulses and for a delay time of roughly 1 ps of the third pulse. The experimental results are well reproduced by optical Bloch equations combined with a phenomenological density-dependent dephasing.