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Quantum Electronics and Laser Science Conference

Influence of exciton line shape asymmetries on four wave mixing spectra of semiconductor microcavities

R. Takayama, N. H. Kwong, Aoki, M. Kuwata-Gonokami, Rudolf H. Binder

Published Jan 1, 2002• 0 citations
Publisher

Abstract

Summary form only given. Using a full microscopic many-body theory, based on the dynamics-controlled truncation (DCT) formalism, we compute four-wave mixing spectra of thin semiconductor quantum well microcavities within the lowest-order nonlinear regime (/spl chi//sup (3)/-regime). Specifically, we focus on heavy-hole 1s excitons and corresponding two-exciton correlations (coherent biexcitons and two-exciton continuum correlations). Within this approach, the linear optical response corresponding to hh-excitons with given absorption lineshapes are inputs to the calculation of the nonlinear FWM spectra.

DOI
10.1109/qels.2002.1031334

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Journal of Experimental and Theoretical Physics•Feb 1, 2006•1 citation
Summary form only given. Using a full microscopic many-body theory, based on the dynamics-controlled truncation (DCT) formalism, we compute four-wave mixing spectra of thin semiconductor quantum well microcavities within the lowest-order nonlinear regime (/spl chi//sup (3)/-regime). Specifically, we focus on heavy-hole 1s excitons and corresponding two-exciton correlations (coherent biexcitons and two-exciton continuum correlations). Within this approach, the linear optical response corresponding to hh-excitons with given absorption lineshapes are inputs to the calculation of the nonlinear FWM spectra.
Summary form only given. The nonlinear optical response in semiconductors has traditionally been treated in a mean field approximation at the 2-particle level. Recent work, in particular comparisons of four-wave mixing (FWM) with microscopic theory, have demonstrated the importance of 4-particle correlations. Such experiments, however, are not optimally sensitive to correlations at the 6-particle level. In order to probe such six-particle correlations we compare the results of six-wave mixing (SWM) measurements with a detailed microscopic theory based on the dynamics controlled truncation scheme (DCT).
Summary form only given. While the conceptual realization of "3-level effects" in semiconductors is usually based on one-particle states given by the band structure of the system, we propose the realization of "3-level effects" in semiconductors based on many-particle states. Specifically, we study the quantum coherences related to excitons and biexcitons. Our analysis is based on the dynamics-controlled trunction (DCT) formalism and includes quantum correlations and quantum coherences within the 3rd-order nonlinear optical response. Within the /spl chi//sup (3)/ regime, only one-pair (excitonic) and two-pair (two-exciton) quantum coherences occur. We restrict the analysis to 1s-hh and 1s-lh excitons which dominate the nonlinear response. Results are shown for ZnSe quantum wells.
This dissertation addresses both fundamental aspects of Coulomb correlations in semiconductor quantum wells and more practical aspects of theoretical analysis of semiconductor optoelectronic devices. After introducing the subject, we present and evaluate a state-of-the-art theory of the third order coherent optical response of a semiconductor quantum well based on the Dynamics Controlled Truncation (DCT) scheme. Already in the third order (the so-called chi (3)) regime, semiconductors exhibit a number of many-body Coulomb correlation effects. Their manifestation in various multi-pulse experimental configurations, customarily used in ultrafast semiconductor spectroscopy, has been an important component of this thesis. Coherent optical effects in a semiconductor 3-band system based on the heavy-hole, light-hole and conduction bands were investigated. The quantum beats in the time-integrated differential transmission signal were analyzed and compared with experimental data obtained at the University of Iowa. Fundamental differences from corresponding quantum beats in atomic 3-level systems were found. Also, the analysis of experimental data (obtained at the University of Arizona) of the coupled heavy-hole-light-hole optical Stark shift revealed evidence of intervalence band coherences, an analog of Raman coherences in atomic 3-levels systems. A scheme for realization of electromagnetically-induced transparency (EIT) based on the interference of excitonic and biexcitonic coherences was proposed. Corresponding experiments performed at the University of Oregon showed indeed a considerable coherent reduction of excitonic absorption. Furthermore, an extension of the chi(3) analysis revealed an energy renormalization of the biexciton, in good agreement with the corresponding experiment. A microscopic analysis of polarization dynamics in time-resolved four-wave mixing signals was performed, revealing interesting implications for the biexciton dephasing in addition to the significance of many-body correlations. In the case of four-wave mixing in semiconductor microcavities, our theoretical analysis in conjunction with experimental data obtained at the University of Tokyo gave us indications for a significant shortcoming of the second Born approximation (2nd BA) applied to two-exciton Coulomb correlations in a thin semiconductor quantum well, in agreement with the general knowledge of the qualitative failure of the 2nd BA in systems with short-range interaction in two dimensions. We also analyzed a novel all-optical switching technique based on the nonlinear polarization rotation. Apart from identifying the many-particle processes relevant for the switch operation in the chi(3) regime, we proposed ways to further optimize the switch.
The combined influence of biexcitons and the two-exciton scattering continuum is analyzed. The analysis is based on a density matrix description of a two-band semiconductor accounting for mean-field contributions, bound biexcitons and the correlated parts of the two-exciton scattering continuum on a common footing. Consistent with the microscopic formulation, the influence of biexcitons as well as that of the two-exciton continuum is represented by a correlation kernel which is obtained from an integral equation. For a one-dimensional model four-wave mixing signals are calculated solving numerically the resulting coupled nonlinear equations for excitation conditions in the vicinity of the 1s resonance. A strong compensation between the exciton–exciton continuum and the mean-field contribution is found for all excitation conditions studied. Surprisingly, biexcitonic signatures turn out to be enhanced when continua are included in the description.
A detailed numerical study of the third-order nonlinear optical susceptibilities (χ(3)) of semiconductor quantum wells is presented. The dependence of χ(3) on material parameters (electron-hole mass ratio and exciton linewidths), on the light polarization configuration (co- and countercircularly polarized) and on the spectral configuration is discussed. The goal of this study is to map out the nonlinear phase shift per quantum well and a related figure of merit caused by quasi-resonant excitonic and biexcitonic nonlinearities induced by picosecond light pulses. The study is based on the dynamics-controlled truncation formalism and evaluated under the assumption that only 1s-heavy-hole excitons contribute to the nonlinearities. It includes all correlation effects (exciton–exciton scattering in the singlet and triplet channels and coherent biexciton formation in the singlet channel) that contribute within the coherent excitonic χ(3) regime.
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.