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physica status solidi (a)

Stimulated Emission of Excitons into Polaritons in a Semiconductor Microcavity Post

F. Tassone, Y. Yamamoto

Published Mar 1, 2000• 4 citations
Publisher

Abstract

Three-dimensional confinement of microcavity polaritons in a small post structure can be used to produce quasi-discrete polariton modes. For sufficiently small structures, the lowest confined polariton mode becomes well isolated from the other states. We consider the exciton–exciton scattering dynamics in the micropost system, and injection of moderate amount of excitons. We show that exciton–exciton scattering provides sufficient gain to produce stimulated emission of excitons into confined polaritons, well before collapse of the Rabi splitting. We also study the statistical properties of this matter laser, and beside usual Poisson statistics and linewidth reduction above threshold, we also find a linewidth increase very far above threshold, which is peculiar of this system, and shows strong similarities to properties of some proposed atomic laser systems.

DOI
10.1002/1521-396x(200003)178:1<119::aid-pssa119>3.0.co;2-u

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Three-dimensional confinement of microcavity polaritons in a small post structure can be used to produce quasi-discrete polariton modes. For sufficiently small structures, the lowest confined polariton mode becomes well isolated from the other states. We consider the exciton–exciton scattering dynamics in the micropost system, and injection of moderate amount of excitons. We show that exciton–exciton scattering provides sufficient gain to produce stimulated emission of excitons into confined polaritons, well before collapse of the Rabi splitting. We also study the statistical properties of this matter laser, and beside usual Poisson statistics and linewidth reduction above threshold, we also find a linewidth increase very far above threshold, which is peculiar of this system, and shows strong similarities to properties of some proposed atomic laser systems.
We consider a semiconductor microcavity etched into a small post structure in which the polariton modes become quantized. When moderate amounts of excitons are injected, large gain for the lowest confined polariton results from exciton-exciton scattering. We show that gain is sufficient to compensate for typical losses of GaAs structures, and stimulated emission of the confined polariton is eventually achieved at an exciton density below that where Rabi splitting collapses. We study the dependence of the threshold exciton density on post size, polariton loss rate and lattice temperature. We study the polariton statistics, and show that far above threshold, typical transition from super-Poissonian to Poissonian statistics is preserved. Exciton-exciton interaction produces a self-phase modulation, resulting in enhanced frequency noise, and into a net increase of the emission linewidth far above threshold. We show how to produce a number-squeezed state using correlation between frequency and number noise. A numerical example of a realistic structure is also analyzed in detail.
The wavefunction of a collection of identical quantum particles of integer spin (bosons) is even under exchange of the coordinates of any two of them. This symmetrization rule of quantum mechanics leads to stimulation of the scattering rate into final states whose population is larger than one. For massless photons, it is routinely observed in the laser. For massive bosons, most previous efforts concentrated in realizing the largely populated equilibrium Bose-Einstein condensate, and observing stimulated emission into it. Here we show that we do not need to produce such a condensate to observe final state stimulation. Instead, we take advantage of the highly non-equilibrium exciton reservoir and of the large polariton populations produced by external laser action on a semiconductor microcavity, and measure final state stimulation of the scattering rate of these excitons into the polaritons.
Summary form only given. Final state stimulation is the origin of amplification in optical lasers and atom lasers. Matter-wave amplification based on an incoherent gain medium has yet to be demonstrated, but is very attractive, particularly for the excitonic system, because electrically injected incoherent excitons can amplify probe excitons without requiring a coherent pump laser. In previous work, we have shown final state stimulation using the exciton-exciton scattering of polaritons in a GaAs based microcavity quantum well; the gain was negligibly small due to the small exciton-exciton scattering rate. However, the rate of exciton-exciton scattering at the exciton saturation density is 9 times larger in CdTe microcavity exciton-polaritons compared to those in GaAs.
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 have performed real and momentum space spectroscopy of exciton polariton condensates in a GaAs-based microcavity under nonresonant excitation with an intensity-stabilized laser. An effective trapping mechanism is revealed, which is due to the stimulated scattering gain inside the finite excitation spot combined with the short lifetime. We observe several quantized modes while the lowest state shows Heisenberg-limited real and momentum space distributions. The experimental findings are qualitatively reproduced by an open dissipative Gross-Pitaevskii equation model.
Dynamics of stimulated scattering of quasi-two-dimensional exciton polaritons in a semiconductor microcavity is considered theoretically. A system possessing a bistable response to coherent excitation is studied. Being a system of weakly interacting Bose particles under strongly nonequilibrium conditions, it exhibits a complex dynamics of the development of condensate modes. It is shown that multimode instability can arise in a threshold way in the system under a smooth increase in pump intensity. In this case, rapid populating of a multitude of unstable modes leads to stochastization of scattering, and evolution to a quasi-steady macrostate is performed as self-organization in an open nonequilibrium system. Arising fluctuations lead to the occurrence of a spatial nonuniformity of the distribution of scattered states.