Quantum theory of polariton weak lasing and polarization bifurcations

The quantum theory of polariton condensation in a trapped state reveals a second-order phase transition evidenced by spontaneous polarization parity breaking in subspaces 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 $g_{xx}^{\left(2\right)}\left(t\right)$, with $g_{xx}^{\left(2\right)}\left(t\right)<1$ over some time intervals, is obtained. Spontaneous symmetry breaking is reflected in the second-order cross correlator of circular polarizations. A related buildup of elliptically polarized weak lasing also results in nonmonotonous dependence of the circular second-order coherence on excitation power and interaction strength.