Collective Excitations, Nambu-Goldstone Modes and Instability of Inhomogeneous Polariton Condensates

We study non-equilibrium microcavity-polariton condensates (MPCs) in a harmonic potential trap theoretically. We calculate and analyze the steady state, collective-excitation modes and instability of MPCs. Within excitation modes, there exist Nambu-Goldstone modes that can reveal the pattern of the spontaneous symmetry breaking of MPCs. Bifurcation of the stable and unstable modes is identified in terms of the pumping power and spot size. The unstable mechanism associated with the inward supercurrent flow is characterized by the existence of a supersonic region within the condensate.