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arXiv:1509.01468

The Connection of Polaritons and Vacuum Rabi Splitting

David W. Snoke

Published Sep 4, 2015• 3 citations
arXivHTMLPDF

Abstract

Polaritons, in particular microcavity exciton-polaritons, have attracted much attention in recent years, as the phenomena of Bose-Einstein condensation and superfluidity have been observed for these quasiparticles. While the basic physics of these systems is well understood, there has been confusion over the connection of these systems to other phenomena, namely the Jaynes-Cummings Hamiltonian, Rabi flopping, and the vacuum Rabi splitting of atoms in a cavity. This paper reviews the basic theory of polaritons and shows these connections explicitly.

DOI
10.48550/arxiv.1509.01468

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Polaritons, in particular microcavity exciton-polaritons, have attracted much attention in recent years, as the phenomena of Bose-Einstein condensation and superfluidity have been observed for these quasiparticles. While the basic physics of these systems is well understood, there has been confusion over the connection of these systems to other phenomena, namely the Jaynes-Cummings Hamiltonian, Rabi flopping, and the vacuum Rabi splitting of atoms in a cavity. This paper reviews the basic theory of polaritons and shows these connections explicitly.
We review, aiming at an audience of final year undergraduates, the phenomena observed in, and properties of, microcavity exciton–polariton condensates. These are condensates of mixed light and matter, consisting of superpositions of photons in semiconductor microcavities and excitons in quantum wells. Because of the imperfect confinement of the photon component, exciton–polaritons have a finite lifetime, and have to be continuously re-populated. Therefore, exciton–polariton condensates lie somewhere between equilibrium Bose–Einstein condensates and lasers. We review in particular the evidence for condensation, the coherence properties studied experimentally, and the wide variety of spatial structures either observed or predicted to exist in exciton–polariton condensates, including quantised vortices and other coherent structures. We also discuss the question of superfluidity in a non-equilibrium system, reviewing both the experimental attempts to investigate superfluidity to date, and the theoretical suggestions of how it may be further elucidated.
Abstract After resuming the basic facts about Bose–Einstein condensation of weakly interacting systems, we review the main experimental and theoretical works aimed at the realization of this intriguing phenomenon in the system of microcavity polaritons. All the experimental results until present suggest that Bose–Einstein condensation is still eluding the experimentalists' efforts. On the theoretical side, only recently polaritons have been described within a quantum field theory of an interacting Bose gas, suggesting that polariton condensation might occur at least as a consequence of polariton parametric scattering under resonant excitation. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
This chapter starts from description of Rabi and Bloch-oscillations in semiconductors. It introduces the exciton-light coupling Hamiltonian in terms of the secondary quantization theory, and considers different approaches to quantum description of light-matter coupling, including the Jaynes-Cummings model and the Dicke model. The crossover from bosonic to fermionic statistics for excitons is then discussed. Finally, the dispersion of exciton-polaritons in microcavities is obtained and the polariton Hamiltonian is constructed.
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).
Exciton-polaritons, mixed light-matter quasiparticles in semiconductors, have recently shown evidence for Bose-Einstein condensation. Some of the properties of condensates of exciton-polaritons are reviewed in this article. We first discuss the spontaneous appearance of long-range order and the way this can be easily accessed in the case of polariton fluids. We show that the Penrose-Onsager criterion is valid even for such a very special case of condensate. We then describe the experiments that allow observation of topological defects in the fluid: quantized vortices, half vortices, and hyperbolic spin vortices. We demonstrate through the comparison with the gross Pitaevskii equation that the appearance and stability of such vortices are linked with the dissipative nature of the condensate together with the presence of disorder. We then briefly summarize the experiments on superfluid behavior of the polaritons at large-enough densities and expand somewhat more on the dynamical behavior of turbulence in the wake of an obstacle, with the appearance of vortex streets. We finally show that the Bogoliubov transformation has been revealed through four-wave mixing experiments.
Recently, several research groups have reported investigations of vacuum-field Rabi splittings (VRS) in the linear response of strongly coupled semiconductor microcavities [1-4]. We have previously reported on the dynamics of time-domain vacuum Rabi oscillations, which are most easily understood in the framework of cavity exciton-polaritons, in which the in-plane momentum k|| is conserved [2], so that at each k|| a single cavity mode interacts with only a single mode of the electromagnetic field (Jaynes-Cummings model). In high Q semiconductor microcavities, the strong coupling between two-dimensional excitons and planar distributed- Bragg-reflector cavity modes results in several-meV splittings observable in the reflectivity or absorption spectrum. In the low excitation regime, the VRS is independent of light intensity incident on the cavity, since the vacuum-Rabi frequency exceeds the externally-driven Rabi frequency (in which case the Jaynes-Cummings model is equivalent to the linear dispersion of the coupled exciton-cavity system). As the incident light intensity is increased, two different effects may be expected to contribute to the nonlinear response. First, as long as the excitonic absorption is equivalent to a two-level system, higher-lying states of the Jaynes-Cummings ladder might be observable. Second, at high intensity phase-space filling and Coulomb screening of the exciton states results in a reduced oscillator strength which leads to a reduced VRS; this effect has no analogue in the case of atom-cavity systems. In this paper, we apply several ultrafast nonlinear techniques to investigate the nonlinear response of semiconductor microcavities.