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physica status solidi (a)

Weak and Strong Coupling for Quantum Boxes in Pillar Microcavities

Giovanna Panzarini, Elisa Molinari

Published Apr 1, 2002• 0 citations
Publisher

Abstract

The interaction of a quantum box with the vacuum field inside a semiconductor pillar microcavity is theoretically investigated by means of a master equation approach accounting also for incoherent relaxation processes. We show that both exciton and biexciton states bound to monolayer fluctuations in narrow quantum wells can be in strong coupling. Finally, we calculate the luminescence spectrum and we explain its structures in terms of transitions between dressed states.

DOI
10.1002/1521-396x(200204)190:2<375::aid-pssa375>3.0.co;2-c

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The interaction of a quantum box with the vacuum field inside a semiconductor pillar microcavity is theoretically investigated by means of a master equation approach accounting also for incoherent relaxation processes. We show that both exciton and biexciton states bound to monolayer fluctuations in narrow quantum wells can be in strong coupling. Finally, we calculate the luminescence spectrum and we explain its structures in terms of transitions between dressed states.
We present a theoretical scheme to investigate the coupled states of a zero-dimensional semiconductor structure and the confined modes of a pillar microcavity, taking into account interacting exciton states and both coherent and incoherent dynamical processes. For quantum-well monolayer fluctuations we find that the frequency of the cavity modes can be tuned in such a way that both exciton and biexciton states are in the strong coupling regime. The calculated luminescence spectra are interpreted in terms of transitions between the dressed states of the composite radiation-matter system.
This chapter attempts to give a review of the main concepts and principal experimental results on semiconductor microcavities in the strong coupling regime. Atomic single-mode interactions in the strong coupling regime were first achieved using Rydberg transitions in the microwave region of the spectrum, and more recently have been achieved using optical transitions. The assumption that the absorption spectrum in bare quantum wells is coincident with the energy distribution of the excitons amounts to an assumption that the excitonic states are localised. The chapter reviews the basic-quantum mechanical model for two-level atoms in a single-mode cavity and its relation to classical linear dispersion theory. Tests of fundamental issues in quantum optics such as quantum measurement theory become possible when the coupled atom-cavity system is in the strong coupling regime and the average number of atoms in the cavity is one.
We analyze the hyper Raman scattering process in a quantum well grown inside a semiconductor microcavity and present a microscopic calculation of emission spectra as a function of excitation energy, detuning, and angles. The exciton-photon coupling is treated non-perturbatively to include polariton effects and the Coulomb interaction between electrons is treated beyond the mean field approximation. The observation of hyper Raman scattering in semiconductor microcavities would represent an important step for the realization of non-classical optical states based on excitons. We find that the polaritons emitted in this scattering process are strongly correlated. This correlation,can be efficiently transferred to output photons, resulting in emission of two correlated non-classical light beams. As a probe of the quantum correlation we calculate the output spectrum of fluctuations in the intensity difference of the two beams generated in the hyper Raman process.
Semiconductor quantum microcavities are interesting physical systems in which fundamental interactions between light and excitons can be explored. For example, in the weak - coupling limit, modified excitonic spontaneous emission can be observed. In the strong-coupling limit, the cavity field modes and the quantum well exciton modes become coupled; the normal modes of the system are "cavity-polaritons" [1,2]. For in-plane wavevectors k// near zero, the normal modes are split by the dipole coupling between the excitons and the cavity vacuum field. This splitting is often referred to as a vacuum-Rabi splitting (VRS), as it has the same physical origin as the VRS observed in the interactions of atoms with single-mode cavities. The physical system in this work consists of a λ planar microcavity formed by two distributed-Bragg reflectors, with five GaAs quantum wells situated in the center of the cavity. In all the experiments described here, the exciton and cavity modes are on resonance (the low-field VRS is 6 meV for this sample).
We discuss the luminescence spectra of coupled light-matter systems realized with semiconductor heterostructures in microcavities in the presence of a continuous, incoherent pumping, when the matter field is fermionic. The linear regime---which has been the main topic of investigation both experimentally and theoretically---converges to the case of coupling to a bosonic material field, and has been amply discussed in the first part of this work. We address here the nonlinear regime, and argue that, counter to intuition, it is better observed at low pumping intensities. We support our discussion with particular cases representative of, and beyond, the experimental state of the art. We explore the transition from the quantum to the classical regime, by decomposing the total spectrum into individual transitions between the dressed states of the light-matter coupling Hamiltonian, reducing the problem to the positions and broadenings of all possible transitions. As the system crosses to the classical limit, rich multiplet structures mapping the quantized energy levels melt and turn to cavity lasing and to an incoherent Mollow triplet in the direct exciton emission for very good structure. Less ideal figures of merit can still betray the quantum regime, with a proper balance of cavity versus electronic pumping.
We provide a unified theory of luminescence spectra of coupled light-matter systems realized with semiconductor heterostructures in microcavities, encompassing (i) the spontaneous emission case, where the system decays from a prepared (typically pure) initial state, and (ii) luminescence in the presence of a continuous incoherent pump. We show how, by provoking a self-consistent quantum state, the pump considerably alters the emission spectra, even at vanishing intensities. The main outcome of our analysis is to unambiguously identify strong coupling in situations where it appears in disguise or only seems to appear. Here, we consider bosonic matter fields, in which case fully analytical solutions can be obtained. This describes the case of quantum wells or large quantum dots, or the limit of low excitation where the probability to have particles in the system remains much smaller than one.