Periodically-driven Floquet time crystal of homogeneous exciton-polariton condensates

We report the presence of photonic Floquet time crystals in a one-dimensional peri odically driven exciton-polariton system. The generation of spontaneous time-translation symmetry breaking is induced by the periodic pumping. We found that in a particular range of the driving period, the Floquet time crystal phase exhibits the period elongation that breaks the time-translation symmetry spontaneously, leading to the subharmonic response that oscillates in a fraction of the drive frequency. The Floquet time crystal phase can be represented in the forms of both exciton and photon densities. The subharmonic oscillation is protected against perturbations and independent of the initial conditons. The photonic time-crystalline ground state can be easily realized in experimental platforms of the exciton-polariton systems that is feasible in room temperatures and has a low excitation threshold compared to conventional photon lasing devices.