Quantum theory of polariton weak lasing and polarization bifurcations

Abstract

The quantum theory of polariton condensation in a trapped state reveals a second-order phase transition evidenced by spontaneous polarization parity breaking in sub-spaces of fixed polariton occupation numbers. The emission spectra of a polariton condensate demonstrate the coexistence of a symmetry-conserving condensate state with {linear} polarization and two symmetry-broken elliptically polarized states in the vicinity of the threshold. As a result, an oscillating linearly polarized second-order coherence $g^{(2)}_{xx}(t)$, with $g^{(2)}_{xx}(t)<1$ over some time intervals is obtained. Spontaneous symmetry breaking is reflected in the second-order cross correlator of circular polarizations. A related build-up of elliptically-polarized weak lasing also results in non-monotonous dependence of the circular second-order coherence on excitation power and interaction strength.