Polarized polariton condensates and coupled XY models

Microcavity polaritons, which at low temperatures can condense to a macroscopic coherent state, possess a polarization degree of freedom. This paper discusses the phase diagram of such a system, showing the boundaries between differently polarized condensates. The Bogoliubov approximation is shown to have problems in describing the transition between differently polarized phases; the Hartree-Fock-Popov approximation performs better, and compares well to exact results that can be used in the limit where the left- and right-circular polarization states decouple. The effects on the phase boundary of various symmetry breaking terms present in real microcavities are also considered.