Phase diagram of microcavity polariton condensates with a harmonic potential trap

• We explore the phase transition in inhomogeneous exciton-polariton condensates with variable pumping conditions.
• A stability boundary is found that is consistent with the turning point of negative to positive iso-potential compressibility.
• A crossover from rigid to soft condensates is found through transition from linear-type excitation to collective Goldstone dispersion.
• The 2D singly trapped polariton condensate may exhibit both the BEC and BKT-like phases, separated by a quasi-condensation boundary.

We theoretically explore the phase transition in inhomogeneous exciton-polariton condensates with variable pumping conditions. Through Bogoliubov excitations to the radial-symmetric solutions of complex Gross–Pitaevskii equation, we determine not only the bifurcation of stable and unstable modes by the sign of fluid compressibility but also two distinct stable modes which are characterized by the elementary excitations and the stability of singly quantized vortex. One state is the quasi-condensate BKT phase with Goldstone flat dispersion; the other state is the localized-BEC phase which exhibits linear-type dispersion and has an excitation energy gap at zero momentum.