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Physical review. B, Condensed matter

Time-integrated four-wave mixing in GaN and ZnSe: Polarization-sensitive phase shift of the excitonic quantum beats

T. Aoki, Georg Mohs, Yuri P. Svirko, Makoto Kuwata‐Gonokami

Published Jul 9, 2001• 7 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.64.045212

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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.
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.
The coherent control of excitonic and biexcitonic polarization in pulse-transmission and four-wave-mixing (FWM) experiments is analysed with real time resolution. As a model system a ZnSe single quantum well is exclusively excited at the heavy-hole exciton and exciton–biexciton resonance. In pulse-transmission experiments the coherent control of excitonic polarization is shown for low excitation intensities. At elevated excitation intensities the dephasing time of the polarization is found to be strongly dependent on the relative phase of two phase-locked laser pulses which perform the coherent manipulation of the polarization. In FWM experiments the separate coherent control of the excitonic and biexcitonic FWM polarization is demonstrated which enables a coherent manipulation of the amplitude and phase of exciton–biexciton beats which are observed on the FWM polarization transients.
The coherent interaction between excitons is revisited by examining the influence of coherent photo-excited excitons on the absorption spectra of ZnSe/ZnMgSSe multiple quantum wells for various polarization configurations. For purely resonant excitation at the heavy-hole exciton, a blueshift of the exciton absorption is found. This distinct blueshift shows a linear dependence on excitation fluence, but with different slopes for different polarization configurations. In the coherent regime the smallest shift is found for an orthogonal linear polarization of the pump and probe, noticeably smaller than the shift for same linear polarization. The strongest shift is found for the same circular polarization. Furthermore, we demonstrate experimentally that pump and probe and four-wave mixing spectra contain equivalent information about the shift and broadening of the exciton line. A linear correlation between the blueshift and the homogeneous linewidth is found in both pump and probe and four-wave mixing.
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 ∑ -+
A systematic analysis of excitonic and biexcitonic contributions to four-wave mixing in dependence on the polarization state and on the intensity of the exciting beams is presented for ZnSe/Zn1—xMgxSySe1—iiy quantum wells. The relative signals of excitons and biexcitons for different polarization configurations are discussed in terms of a microscopic density matrix model revealing excellent correspondence to the complex experimental data. In configurations which do not allow for a third-order contribution of the biexciton of zero angular momentum higher-order correlations are shown to become important already at densities as low as 1010 excitons cm—2/pulse.