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Effects of bound and scattered two-exciton states in polarization-sensitive four-wave mixing

Yuri P. Svirko, T. Aoki, C. Ramkumar, Ryo Shimano, Makoto Kuwata‐Gonokami

Published May 12, 2000• 0 citations
OpenAlex

Abstract

Summary form only given. Four-particle correlation mediated by the Coulomb interaction has been found to play a major role in the nonlinear optical response at the semiconductor band edge at low excitation density. The attractive interaction of the excitons with opposite spins result in the formation of bound (bi-exciton) and unbound (scattered) two-exciton states. In this paper we report on the first to our knowledge, comparison of the contributions to the coherent nonlinearity from the bound and unbound two-exciton states. The polarization-sensitive four wave mixing experiment is performed in the high-Q semiconductor microcavity, in which the incoherent effects are suppressed due to strong exciton-photon coupling. The semiconductor microcavity has a single 12-nm-thick GaAs quantum well.

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Correlations due to biexcitons as well as to two-pair scattering states are direct manifestations of Coulomb quantum kinetics. Effects resulting from the memory structure of the corresponding contributions to the optical interband polarization are analyzed taking a ZnSe single-quantum well as model system. Our calculations are based on a microscopic density matrix description using the dynamics controlled truncation scheme for closing the hierarchy of higher-order density matrices. A detailed comparison between experiment and theory allows for the identification of numerous effects directly reflecting different aspects of pair-correlations. In particular, we demonstrate various influences of the two-pair scattering continuum on four-wave-mixing signals. Furthermore, we show that signals with a dynamically changing polarization sensitively monitor a competition between coherent parts of the dynamics and signal components induced by incoherent exciton densities. Surprisingly, the phase of these signals is found to be almost unaffected by the presence of incoherent densities. This result can be traced back to a compensation of the influences on the phases resulting from different incoherent parts of the dynamics. Six-particle correlations representing transitions from incoherent densities to two-pair correlations turn out to be indispensable for a proper description of this effect.© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

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Signatures of the excitonic memory effects in four-wave mixing processes in cavity polaritons

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We report the signatures of the exciton correlation effects with finite memory time in frequency domain degenerate four-wave mixing (DFWM) in semiconductor microcavity. By utilizing the polarization selection rules, we discriminate instantaneous, mean-field interactions between excitons with the same spins, long-living correlation due to the formation of biexciton state by excitons with opposite spins, and short-memory correlation effects in the continuum of unbound two-exciton states. The DFWM spectra give us the relative contributions of these effects and the upper limit for the time of the exciton-exciton correlation in the unbound two-exciton continuum. The obtained results reveal the basis of the cavity polariton scattering model for the DFWM processes in high-$Q$ GaAs microcavity.

arXiv:cond-mat/0003145•Physical review. B, Condensed matter•Sep 15, 2000•12 citations
Summary form only given. Four-particle correlation mediated by the Coulomb interaction has been found to play a major role in the nonlinear optical response at the semiconductor band edge at low excitation density. The attractive interaction of the excitons with opposite spins result in the formation of bound (bi-exciton) and unbound (scattered) two-exciton states. In this paper we report on the first to our knowledge, comparison of the contributions to the coherent nonlinearity from the bound and unbound two-exciton states. The polarization-sensitive four wave mixing experiment is performed in the high-Q semiconductor microcavity, in which the incoherent effects are suppressed due to strong exciton-photon coupling. The semiconductor microcavity has a single 12-nm-thick GaAs quantum well.
The coherent response of excitons in semiconductor nanostructures measured in four-wave mixing (FWM) depends strongly on the inhomogeneous broadening of the exciton transition. We investigate GaAs/Al0.3Ga0.7As single quantum wells (SQW) and AlxGa1-xAs mixed crystals. Additional to the usual phase-space filling nonlinearity, excitation-induced dephasing (EID) and biexciton formation (BIF) are important. EID leads to a strong dependence of the signal on the angle between the linear input polarizations. We find that EID persists in inhomogeneous systems, showing that the mutual density-dependent dephasing rate difference between two subsystems within the inhomogeneous distribution is strongly dependent on their energy difference. BIF is strongly affecting the cross-linear polarized FWM response. The signal for positive delay is dominated by the transitions from the one-exciton state X to the two-exciton states. Here, the third-order polarization at X-XX is not at the same resonance as the first-order polarization at 0-X. Consequently, the rephasing of the microscopic third-order polarization to the macroscopic FWM photon echo is blurred by the non-perfect correlation of X and XX energies, leading to a fast and non-exponential signal decay in delay time. For inhomogeneous broadenings larger than the biexciton binding energy, we find an enhanced biexciton binding energy, and a quenching of the oscillator strength of the unbound biexciton.
The paper presents a description of two-pair correlations in an electron-hole system in laser-excited direct-gap semiconductors in terms of the exciton-boson formalism. The dependence of the states of quasi-particles on their angular momentum orientation is properly taken into account following group theory rules. It is shown for the example of heavy hole excitons in GaAs quantum wells that Coulomb two-exciton correlations include effective repulsion between excitons with nonzero total momenta and effective attraction between excitons with zero total momenta. They generate exciton and biexciton nonlinearities, respectively, in the exciton-biexciton system. The Heisenberg equations of motion derived are applied to four-wave mixing in the coherent mode. Two components of Coulomb two-exciton correlations were found to generate coherent four-wave mixing either separately, one at the cocircular and the other at the perpendicular-linear polarization of applied pulses, or jointly at parallel-linear polarization. General equations are obtained for the amplitude of four-wave mixing signals with time resolution in these polarization configurations, which, in the limit of ultranarrow pulses, reduce to analytic functions of time and excitation and sample parameters. These equations are used to analyze signal characteristics in every polarization configuration. The results give a correct picture of biexciton effects and the polarization dependence of coherent four-wave mixing in GaAs quantum wells.
The nonlinear optical responses of a strongly coupled exciton-photon system in a semiconductor microcavity structure under weak excitation can be explained by a weak exciton-exciton interaction due to the nonideal bosonic (weakly interacting bosons) nature of the excitons. The exciton-exciton interaction leads to an attractive interaction between excitons with opposite spin, and a repulsive interaction between excitons with the same spin and a phase space filling. Earlier, we have reported the ratio of these interaction energies from the polarization-sensitive degenerate four-wave mixing on a strongly coupled GaAs quantum well (QW) microcavity under weak excitation density. In order to quantitatively determine the exciton-exciton polarization interaction energy, we have proposed a pump-probe nonlinear polarization rotation scheme. In the paper, we report the quantitative measurement of the exciton-exciton polarization interaction energy in the above mentioned system under strict weak excitation density using the pump-probe nonlinear polarization rotation (PR) technique. In the technique, the change of polarization state of a weak linearly polarized probe due to the anisotropy induced by a strong, circularly polarized pump is monitored in reflection geometry.
Summary form only given. The ultrafast nonlinear optical response of semiconductor-microcavities (SMCs) in the nonperturbative regime is attracting growing interest for exploring fundamental light-matter interactions in many-particle quantum systems, as well as for the future implementations of ultrafast photonic devices. In spite of many investigations, the coherent dynamics of excitonic nonlinear-response in the nonperturbative regime has not been fully understood. Open questions are how strong exciton-cavity coupling affects exciton-exciton (X-X) interactions, and how in turn the X-X correlation influences the nonlinear response of SmCs. We investigate these open questions and show that the nonperturbative regime provides an unprecedented tool for investigating four-particle correlations.We start from the equations for the third order exciton polarization and cavity field describing quantum optical effects and coherent nonlinear optics in SMCs, perform the semiclassical factorization and include multiple scattering processes.
Correlations due to biexcitons as well as to two-pair scattering states are direct manifestations of Coulomb quantum kinetics. Effects resulting from the memory structure of the corresponding contributions to the optical interband polarization are analyzed taking a ZnSe single-quantum well as model system. Our calculations are based on a microscopic density matrix description using the dynamics controlled truncation scheme for closing the hierarchy of higher-order density matrices. A detailed comparison between experiment and theory allows for the identification of numerous effects directly reflecting different aspects of pair-correlations. In particular, we demonstrate various influences of the two-pair scattering continuum on four-wave-mixing signals. Furthermore, we show that signals with a dynamically changing polarization sensitively monitor a competition between coherent parts of the dynamics and signal components induced by incoherent exciton densities. Surprisingly, the phase of these signals is found to be almost unaffected by the presence of incoherent densities. This result can be traced back to a compensation of the influences on the phases resulting from different incoherent parts of the dynamics. Six-particle correlations representing transitions from incoherent densities to two-pair correlations turn out to be indispensable for a proper description of this effect.© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
We report the signatures of the exciton correlation effects with finite memory time in frequency domain degenerate four-wave mixing (DFWM) in semiconductor microcavity. By utilizing the polarization selection rules, we discriminate instantaneous, mean-field interactions between excitons with the same spins, long-living correlation due to the formation of biexciton state by excitons with opposite spins, and short-memory correlation effects in the continuum of unbound two-exciton states. The DFWM spectra give us the relative contributions of these effects and the upper limit for the time of the exciton-exciton correlation in the unbound two-exciton continuum. The obtained results reveal the basis of the cavity polariton scattering model for the DFWM processes in high-QQQ GaAs microcavity.