Time Crystal in a Single-mode Nonlinear Cavity

Abstract

Time crystal is a class of non-equilibrium phases with broken time-translational symmetry. Here we demonstrate the time crystal in a single-mode nonlinear cavity. The time crystal originates from the self-oscillation induced by a linear gain and is stabilized by a nonlinear damping. We show in the time crystal phase there are sharp dissipative gap closing and pure imaginary eigenvalues of the Liouvillian spectrum in the thermodynamic limit. Dynamically, we observe a metastable regime with the emergence of quantum oscillation, followed by a dissipative evolution with a time scale much smaller than the oscillating period. Moreover, we show there is a dissipative phase transition at the Hopf bifurcation of the model, which can be characterized by the photon number fluctuation in the steady state. These results pave a new promising way for further experiments and deepen our understanding of time crystals.

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Cited by in corpus (4)

• Boundary Time Crystals Induced by Local Dissipation and Long-Range Interactions
• Impact of quantum noise on phase transitions in an atom-cavity system with limit cycles
• Exact steady state of quantum van der Pol oscillator: critical phenomena and enhanced metrology
• Continuous time crystals as a PT symmetric state and the emergence of critical exceptional points