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Many-Body Quantum Theory of Spontaneous Emission of Semiconductor Quantum Wells

S. Kuckenburg, Angela Thränhardt, A. Knorr, M. Kira, F. Jahnke, S. W. Koch

Published Mar 1, 2000• 2 citations
Publisher

Abstract

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.

DOI
10.1002/1521-396x(200003)178:1<409::aid-pssa409>3.0.co;2-m

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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.
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.
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.
A microscopic many-body theory for the optical and electronic properties of semiconductors is reviewed with an emphasis on the role of correlation effects. At the semiclassical level, the semiconductor Bloch equations include many-body effects via bandgap and field renormalization as well as correlation contributions representing two electron-hole pair amplitudes, excitonic populations, and coupled interband and intraband coherences. These Coulomb interaction induced carrier correlations lead to characteristic signatures in nonlinear semiconductor spectroscopy. At the fully quantum mechanical level the dominant light-matter correlations are described by coupled semiconductor Bloch and luminescence equations. Excitonic emission properties of quantum well and microcavity systems are discussed, including effects such as coherent signatures in the secondary emission and coherent control of the emitted light.
The spontaneous emission rate of a quantum dot coupled to a structured photonic reservoir is determined by the frequency dependence of its local density of photon states. Through phonon-dressing, a breakdown of Fermi's golden rule can occur for certain photonic structures whose photon decay time becomes comparable to the longitudinal acoustic phonon decay times. We present a polaron master equation model to calculate the photoluminescence intensity from a coherently excited quantum dot coupled to a structured photonic reservoir. We consider examples of a semiconductor microcavity and a coupled cavity waveguide, and show clear photoluminescence intensity spectral features that contain unique signatures of the interplay between phonon and photon bath coupling.
The discussions in the previous chapters show that already the spontaneous emission, i.e., the simplest manifestation of the quantum-optical fluctuations, exhibits highly nontrivial features as soon as the quantum light is coupled to interacting many-body systems. We have seen, for example, that pronounced resonances in the semiconductor luminescence originate from a nontrivial mixture of exciton and plasma contributions in contrast to the simple transitions between the eigenstates of isolated atomic systems. As a consequence of the conservation laws inherent to the light–matter coupling, the photon emission induces rearrangements in the entire many-body system leading, e.g., to pronounced hole burning in the exciton distribution. As discussed in Chapter 29, this depletion of the optically active excitons leads to a reduction of the total radiative recombination and the appearance of nonthermal luminescence even when the electron–hole system is in quasiequilibrium. Already these observations show that the coupled quantum-optical and many-body interactions induce new intriguing phenomena that are not explainable by the concepts of traditional quantum optics or classical semiconductor physics alone. The foundations of quantum optics are based on systematic investigations of simple systems interacting with few quantized light modes. In this context, one can evaluate and even measure the exact eigenstates or the density matrix with respect to both the photonic and the atomic degrees of freedom. In semiconductor systems, currently the investigations using one or a few quantum dots (QD) are closest to the atomic studies because, due to their discrete eigenstates, one can treat strongly confined quantum dots to some extent like artificial atoms.
The dynamics of semiconductor quantum wires and wells that are coupled to a single-mode quantum field are analyzed. Within a two-band tight-binding model the Coulomb interaction between electrons and holes is included on a microscopic basis and the light-matter interaction is quantized. The dynamics of the system is described by equations of motion for the relevant set of expectation values of the coupled electronic-photonic system. Starting from the initial condition of a single photon occupying the field mode, we study the dynamics of the mean photon number. To analyze effects arising from the many-body Coulomb interaction, we use an exact truncation of the electronic hierarchy problem by employing the fact that N photons cannot excite more than N electron-hole pairs. We compare Rabi oscillations with and without Coulomb interaction for different excitation conditions. When the quantum field mode is initially occupied by two photons, two interacting electron-hole pairs, i.e., biexcitons, can be generated which characteristically modify the dynamics. Within a consistent and fully-quantized approach we show consequences of biexcitonic many-body correlations that are coupled to a quantum field and discuss the obtained dynamics.