Josephson effects in condensates of excitons and exciton polaritons

We analyze theoretically the phenomena related to the Josephson effect for exciton and polariton condensates, taking into account their specific spin degrees of freedom. We distinguish between two types of Josephson effects: the extrinsic effect, related to the coherent tunneling of particles with the same spin between two spatially separated potential traps, and the intrinsic effect, related to the ``tunneling'' between different spinor components of the condensate within the same trap. We show that the Josephson effect in the nonlinear regime can lead to nontrivial polarization dynamics and produce spontaneous separation of the condensates with opposite polarization in real space.