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Josephson effects in condensates of excitons and exciton polaritons. I. A. Shelykh, D. D. Solnyshkov, G. Pavlovic and G. Malpuech in Phys. Rev. B 78:041302(R) (2008).  What the paper says!?

The Authors study the «the Josephson effects for excitons and polaritons, related to the tunneling between two condensates possessing macroscopic phase coherence» with a focus on spin and thus polarization:

The important peculiarity of optically active two- dimensional (2D) excitons and polaritons is linked with their spin structure: they have two allowed spin projections on the structure growth axis, related to the right-circular and left- circular polarization of the counterpart photons. Moreover, due to the effects of exchange, the interparticle interactions are strongly spin anisotropic:8,9 particles with similar spin projections strongly repel, while particles with opposite spin

projections almost do not interact with each other.

They highlight the role of interactions:

The crucial property of the condensates of cold atoms and the condensates of excitons and polaritons, as compared to the superconductors, is the interaction between the tunneling particles. This leads to the striking nonlinear effects in Jo- sephson dynamics, such as anharmonicity of the Josephson oscillations19 and macroscopic quantum self-trapping (MQST) in the case, when the initial imbalance between the

two condensates exceeds some critical value

The details of polarization are interesting but I don't cover them now.