Quantum statistics of polariton condensates in the weak lasing regime

We study theoretically the quantum statistics of exciton-polaritons accumulated in two bosonic condensates linked with a coherent (Josephson) and dissipative channel. The weak lasing regime characterized by spontaneous symmetry breaking has been predicted for this system within the mean field approximation. Here we go beyond the mean field theory and show that the weak lasing regime also manifests itself in dramatic changes in the statistics of both condensates that may be revealed in measurements of the second-order coherence. Namely, the condensates experience a superbunching at large enough external pumping and the cross-correlation reveals an anti-bunching effect at low enough pumping.