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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Single quantum dots in microcavities

Fabrice P. Laussy, Михаил Михайлович Глазов, Alexey Vitalievich Kavokin, G. Malpuech

Published Aug 31, 2006• 0 citations
Publisher

Abstract

In 2004 two groups have reported observation of the strong coupling regime in 3D microcavities with single quantum dots (QD). We present the quantum theory of non-linear emission of photons by such structures. We derive the exciton creation operator which coincides with a Fermi one for QDs smaller than the exciton Bohr radius and with Bose one for very large QDs. In intermediate size dots excitonic statistics is in between the Fermi and Bose ones. Consequently, the non-linear optical spectra change from the Mollow triplet in the fermionic case to the Rabi doublet in the bosonic case. We predict appearance of a characteristic multiplet structure of the non-linear emission in the intermediate regime.

DOI
10.1117/12.675924

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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.
A single atom in a cavity is the model system of cavity quantum electrodynamics (CQED). The strong coupling regime between the atom and cavity-confined photon corresponds to the reversible exchange of energy between the two modes, and underpins a wide range of CQED phenomena with applications in quantum information science, including for example as quantum logic gates and as sources of entangled states. An important advance was achieved recently when strong coupling between excitons and cavity photons was reported for the first time for localized quantum dots (QDs) in micron-size solid state cavities. This has significance in terms of scalability and integration with other optical devices, and could lead to the emergence of "quantum optics on a chip" technology. However the results presented so far for quantum dots are in the linear regime, corresponding to coupling to the vacuum field (vacuum Rabi splitting); they are not a true QED effect and can equally well be described by classical physics as the coupling between two oscillators. In this paper, we present evidence for a purely quantum phenomenon for the QD/cavity photon system, namely the increase in splitting of the levels when the mean number of photons in the cavity is increased. This corresponds to non-linearities on the single-photon scale: the presence of a single excitation in the cavity changes the level structure, affecting the emission energies for a second photon. Such results are a first step in demonstrating the promise of quantum dots for CQED applications.
We present an overview of the model we developed (F. P. Laussy et al., cond-mat/0505728 [1]) to describe strong coupling of light with excitons hosted by large quantum dots, where the number of excitons is eventually limited by Pauli blocking of the underlying electron-hole structure. We apply it to a limiting case not investigated before, where excitations are created in states analogous of Dicke states describing non-interacting distinguishable fermionic excitations coupled through the radiation field. The multiplet structures in the optical emission spectra which we obtain show, by comparison with our previous results, that they remain essentially the same independently of the model for small saturation numbers, while they acquire specificities of their own when the number of allowed excitons becomes large. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)