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Quantum Electronics and Laser Science Conference

On the interplay between excitonic and biexcitonic quantum coherences

I. Rumyantsev, Rolf H. Binder, Ryu Takayama, N.H. Kwong

Published Jan 1, 2002• 0 citations
Publisher

Abstract

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.

DOI
10.1109/qels.2002.1031411

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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.
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.
A theoretical analysis of intervalence-band coherences is presented. These optically created non-radiative coherences are generalizations of non-radiative coherences in atomic and molecular three-level systems. Whereas in three-level systems these coherences are the basis of important and well-established nonlinear effects, the interpretation of experimental evidence for such coherences in semiconductors needs to be supported by many-body theory. Based on the dynamics-controlled truncation formalism, the respective contributions of intervalence-band coherences and coherent biexcitonic correlations in time-integrated differential transmission spectroscopy is investigated. It is found that the contribution of the biexcitonic correlations to the observable heavy-hole–light-hole beats can be eliminated, either by reducing the light pulse duration or by choosing the central frequency of the light pulses at the heavy-hole exciton.
Summary form only given. The nonlinear optics near the fundamental absorption edge is commonly formulated in terms of a limited number of material parameters characterizing the strength of specific nonlinear processes. Once the nonlinear response function underlying these material parameters is known, one can optimize the relevant nonlinear optical effect for specific device applications. This study is focused on optical nonlinearities at quasi-resonant conditions in the picosecond-pulse regime, where excitonic correlations, such as biexcitonic resonances, contribute prominently to the physical processes. Using a microscopic theory, we have calculated systematically the parameter dependencies of some representative figures of merit, nonlinear phase shift /spl Delta//spl phi/ and differential transmissivity AT, which provide complementary information on the nonlinear susceptibility-/spl chi//sup (3)/:/spl Delta//spl phi//spl sim/Re/spl chi//sup (3)/, /spl Delta/T/spl sim/Im/spl chi//sup (3)/, approximately. We will show in detail how the various aspects of excitonic dynamics affect these quantities around the exciton resonance.
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.
A theoretical study of the coherently coupled heavy-hole--light-hole optical Stark effect in semiconductor quantum wells is presented. Based on a detailed investigation of the various many-body contributions to the Stark shifts, we identify a parameter regime in which the existence of intervalence band coherences (analogous to the nonradiative Raman coherence in three-level atoms) can be inferred from the coherently coupled heavy-hole--light-hole excitonic optical Stark shift. The analysis is performed for the third-order nonlinear optical regime $({\ensuremath{\chi}}^{3}$ regime), and is based on the dynamics-controlled truncation (DCT) formalism. It includes the relevant optical selection rules, excitonic and two-exciton-correlation (e.g., biexcitonic) effects.