Supersolidity of Polariton Condensates in Photonic Crystal Waveguides

Condensation of exciton polaritons has been recently observed in gap-confined states of one-dimensional photonic crystal waveguides. Here we focus on the theoretical emergence of a second emission threshold in this platform, in addition to the one associated with condensation at zero momentum, due to the nonlinear polariton scattering from the condensate into finite momentum eigenmodes. The physics of this spatially modulated condensate is related to a spontaneous breaking of both phase and translational symmetries simultaneously, bearing similarities with the highly sought supersolid phase in Helium and ultracold atomic gases but with a novel mechanism typical of the driven-dissipative scenario. We then propose clear-cut and unequivocal experimental signatures that would allow to identify such non-equilibrium supersolidity of polariton condensates.