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Conference on Lasers and Electro-Optics

Theory of secondary emission and exciton formation in semiconductor quantum wells

S. Kuckenburg, Angela Thränhardt, A. Knorr, S. W. Koch

Published Aug 29, 2005• 0 citations
Publisher

Abstract

Summary form only given. The light emission of optically excited quantum well excitons can be divided into two parts: the nonscattered contribution (primary emission, where the momentum of the photon is conserved) and the scattered one (secondary emission). Recent theoretical work was focused on isolated mechanisms for the generation of secondary emission, such as exciton-disorder (Rayleigh signal), exciton-phonon and exciton-photon interactions. In extension of these studies, we treat a more general situation by studying the simultaneous action of several emission generating mechanisms for the ease of 1s-exciton excitation in the low density case. The theoretical approach is based on a coupled set of Heisenberg equations of motion for quantum correlation functions of excitons, photons, phonons and their assisted density matrices in a disordered system using 2nd order Born and Markovian approximation. First, we illustrate the procedure and numerical results for a coupled system of excitons, phonons and photons in an ordered quantum well.

DOI
10.1109/iqec.2000.907870

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•Jan 1, 2005•0 citations
Summary form only given. The light emission of optically excited quantum well excitons can be divided into two parts: the nonscattered contribution (primary emission, where the momentum of the photon is conserved) and the scattered one (secondary emission). Recent theoretical work was focused on isolated mechanisms for the generation of secondary emission, such as exciton-disorder (Rayleigh signal), exciton-phonon and exciton-photon interactions. In extension of these studies, we treat a more general situation by studying the simultaneous action of several emission generating mechanisms for the ease of 1s-exciton excitation in the low density case. The theoretical approach is based on a coupled set of Heisenberg equations of motion for quantum correlation functions of excitons, photons, phonons and their assisted density matrices in a disordered system using 2nd order Born and Markovian approximation. First, we illustrate the procedure and numerical results for a coupled system of excitons, phonons and photons in an ordered quantum well.
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 present a bosonic description of excitons created by means of resonant optical pumping in a quantum well in the presence of a weak disorder potential. The excitonic collective state is a Glauber coherent state, closely related to that of photons but substantially different from that of few-level models. The theory, applying to the low-density regime, is used to explain various transient linear optical experiments involving resonantly excited excitons in GaAs quantum wells. In particular, we consider coherent control of the exciton density and spin, resonant Rayleigh scattering and scattering coherent control. Our quantum mechanical approach for light emission shows that excitonic secondary emission has a coherent component, in agreement with experiments.
A fully microscopic quantum theory for the photoluminescence of a semiconductor quantum well is summarized. The dynamic equations for the interacting electron–hole pairs (excitons), phonons and photons are presented and specialized for the situations of interacting electron–hole populations and low density excitonic populations. Signatures of phonon assisted exciton formation are discussed in the low density limit, where the early dynamics is found to be strongly dependent on the emission angle. For long times the decay can be described by an angle-independent decay rate.
Electron-phonon coupling in semiconductor quantum dots plays a significant role in determining the optical properties of excited excitons, especially the spectral nature of emitted photons. This paper presents a comprehensive theory and analysis of emission spectra from artificial atoms or quantum dots coupled to structured photon reservoirs and acoustic phonons, when excited with incoherent pump fields. As specific examples of structured reservoirs, we chose a Lorentzian cavity and a slow-light coupled-cavity waveguide, which have both been explored experimentally. For the case of optical cavities, we directly compare and contrast the spectra from three well-known and distinct theoretical approaches to treat electron-phonon coupling, including a Markovian polaron master equation, a non-Markovian phonon correlation expansion technique, and a semiclassical linear susceptibility approach, and we point out the limitations of these models. For the cavity-QED polaron master equation, which treats the cavity-mode operator at the level of a system operator, we give closed form analytical solutions to the phonon-assisted scattering rates in the weak excitation approximation, fully accounting for temperature, cavity-exciton detuning, and cavity-dot coupling. We also show explicitly why the semiclassical linear susceptibility approach fails to correctly account for phonon-mediated cavity feeding. For weakly coupled cavities, we calculate the optical spectra using a more general photon reservoir polaron master-equation approach, and explain its differences from the above approaches in the low-QQQ limit of a Lorentzian cavity. We subsequently use this general reservoir approach to calculate the emission spectra from quantum dots coupled to slow-light photonic crystal waveguides, which demonstrate a number of striking photon-phonon coupling effects.
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.
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.