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.

• Received 6 January 2000

DOI:https://doi.org/10.1103/PhysRevA.62.063809