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We analyse nonequilibrium phase transitions in microcavity polariton condensates trapped in optically induced annular potentials. We develop an analytic model for annular optical traps, which gives an intuitive interpretation for recent experimental observations on the polariton spatial mode switching with variation of the trap size. In the vicinity of polariton lasing threshold we then develop a nonlinear mean-field model accounting for interactions and gain saturation, and identify several bifurcation scenarios leading to formation of high angular momentum quantum vortices. For experimentally relevant parameters we predict the emergence of spatially and temporally ordered polariton condensates (time crystals), which can be witnessed by frequency combs in the polariton lasing spectrum or by direct time-resolved optical emission measurements. In contrast to previous realizations, our polaritonic time crystal is spontaneously formed from an incoherent excitonic bath and does not inherit its frequency from any periodic driving field.
We investigate an optically trapped exciton-polariton condensate and observe temporal coherence beyond 1~ns duration. Due to the reduction of the spatial overlap with the thermal reservoir of excitons, the coherence time of the trapped condensate is
Superposition states of circular currents of exciton-polaritons mimic the superconducting flux qubits. The phase of a polariton fluid must change by an integer number of $2pi$, when going around the ring. If one introduces a ${pi}$-phase delay line i
Tunable spin correlations are found to arise between two neighboring trapped exciton-polariton condensates which spin-polarize spontaneously. We observe a crossover from an antiferromagnetic- to a ferromagnetic pair state by reducing the coupling bar
We investigate the thermal robustness of traveling polariton condensates. We create remote condensates that have never been in contact, and study their interference in momentum space, when they travel with the same velocity, by means of time-resolved
Coherent bosonic ensembles offer the promise of harnessing quantum effects in photonic and quantum circuits. In the dynamic equilibrium regime, the application of polariton condensates is hindered by exciton-polariton scattering induced de-coherence