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Quantum Electronics and Laser Science Conference

Adiabatic following of incoherent exciton density in semiconductor quantum wells

Zhenshan S. Yang, Rudolf H. Binder, N. H. Kwong, Ryu Takayama

Published Jan 1, 2002• 0 citations
Publisher

Abstract

Summary form only given. Effects of exciton-exciton correlations (e.g. bound biexciton, exciton-exciton scatterings) have been amply demonstrated in the /spl chi//sup (3)/ contributions to experiments measuring the interband polarization in semiconductor quantum wells. Increasing attention is currently being focussed on higher order excitonic correlation effects. One higher-order quantity is the incoherent exciton density (defined as total exciton density minus the interband polarization squared) which is created by excitons scattering each other out of the coherent component. Other than its role in the dephasing and relaxation of the system, the incoherent exciton density has not received much attention. In this contribution, we present results of our theoretical study on the behavior of this quantity and related correlation functions under conditions that inhibit relaxation. Our theory follows the general formulation of bosonic theories for excitons: the basic degrees of freedom are exact bosons, and the fermionic exchange effects are incorporated into the boson-boson and boson-photon effective Hamiltonians. We truncate the effective interaction at the two-boson level. No formal bosonization procedure is used: the matrix elements of our effective Hamiltonian are chosen in such a way that in the coherent /spl chi//sup (3)/ limit, our boson theory yields formally identical results as the standard fermionic dynamics controlled truncation formalism. Standard many-body techniques are used to derive equations of motion for densities, correlation functions, and measurable quantities such as the interband polarization.

DOI
10.1109/qels.2002.1031338

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Summary form only given. Effects of exciton-exciton correlations (e.g. bound biexciton, exciton-exciton scatterings) have been amply demonstrated in the /spl chi//sup (3)/ contributions to experiments measuring the interband polarization in semiconductor quantum wells. Increasing attention is currently being focussed on higher order excitonic correlation effects. One higher-order quantity is the incoherent exciton density (defined as total exciton density minus the interband polarization squared) which is created by excitons scattering each other out of the coherent component. Other than its role in the dephasing and relaxation of the system, the incoherent exciton density has not received much attention. In this contribution, we present results of our theoretical study on the behavior of this quantity and related correlation functions under conditions that inhibit relaxation. Our theory follows the general formulation of bosonic theories for excitons: the basic degrees of freedom are exact bosons, and the fermionic exchange effects are incorporated into the boson-boson and boson-photon effective Hamiltonians. We truncate the effective interaction at the two-boson level. No formal bosonization procedure is used: the matrix elements of our effective Hamiltonian are chosen in such a way that in the coherent /spl chi//sup (3)/ limit, our boson theory yields formally identical results as the standard fermionic dynamics controlled truncation formalism. Standard many-body techniques are used to derive equations of motion for densities, correlation functions, and measurable quantities such as the interband polarization.
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.
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.
This dissertation addresses both fundamental aspects of the coherent exciton kinetics in single semiconductor quantum wells and more application-oriented aspects of the collective excitonic optical properties in quantum well Bragg structures. We use a bosonic theory to investigate the ultrafast coherent exciton dynamics after an optical excitation in a single semiconductor quantum well. It is shown that, on intermediate time scales, nonlinear mean-field interactions between excitons lead to a coherent, wave-like evolution in the momentum distribution of optically inactive excitons, which can survive for some time before dephasing sets in. Driven by two-exciton correlations, this coherent quantum kinetic effect bridges the well-known kinetics associated with optical excitation on the one hand and incoherent relaxation on the other. We also study more general dynamical properties of bosonic mean field systems with N-species of excitons (in a single semiconductor quantum well). We find that the momentum-conserving exciton mean field equations, including the coupling to external fields and fermionic corrections, have the dynamical structure su(N,N). We show that one can define a non-real generalized "Bloch vector" and a non-hermitian "density matrix" description, which allow us to explicitly obtain all the constants of motion associated with the su(N,N) symmetry. The many-body effects and correlations of excitons in a single quantum well are mainly induced by the Coulomb interactions. In the case of a semiconductor quantum well Bragg structure, the light induced coupling between different quantum wells also dramatically affects the excitons' behavior, especially through the collective excitations of excitons in the whole structure. We investigate the linear excitonic optical properties of the quantum well Bragg structure induced by the collective excitations using the transfer matrix approach. We show that the so called "intermediate band" (IB) created by the exciton resonance, which does not exist in conventional photonic crystals, can be used for the stopping, storing and releasing of light, which is important in information processing devices. We also discuss the compensation of the dispersive distortion in the light delay process through reversing the IB band structure. Other conceptual and practical issues such as the decay rate of the IB modes and the generalized anti-reflection coating are also investigated.
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 phonon scattering assisted luminescence of semiconductor quantum well excitons after short pulse excitation is investigated. The presented analysis is based on the low-density limit of a set of equations for quantum correlation functions for electrons, phonons, and photons. The dynamics of the correlation functions describes the optical excitation and the decay of the coherent exciton polarization as well as the generation of an incoherent exciton occupation and its luminescence decay. Numerical solutions of the equations of motion demonstrate strong competition effects of the exciton-phonon and the exciton-photon interaction on a picosecond time scale and lead to a nonmonotonous temperature dependence of the time-resolved spontaneous emission. The angle resolved emission resembles the generation and decay dynamics of the exciton density for different in-plane momenta.
We develop a heirarchy of equations that describes the electrodynamics of the semiconductor band edge. An exciton basis that incorporates intrapair Coulomb interaction is used. The excitons are treated as quasibosons that satisfy commutation relations intermediate between bosonic and fermionic. Their nonlinear dynamics are a consequence of phase-space filling and an effective exciton-exciton interaction that depends only on their center-of-mass wave vectors and internal quantum numbers. The resulting expansion in powers of the optical field is analogous to Axt and Stahl's dynamically controlled truncation, but takes a simpler form. If damping is omitted or if all interband and intraband dephasing time constants are the same, we find a set of relationships among the interband and intraband correlation functions which in the free pair basis give the semiconductor Bloch equations.