We study an emergent semiclassical time crystal composed of two interacting driven-dissipative bosonic modes. The system has a discrete $\mathbb Z_2$ spatial symmetry which, depending on the strength of the drive, can be broken in the time-crystalline phase or it cannot. An exact semiclassical mean-field analysis, numerical simulations in the quantum regime, and the spectral analysis of the Liouvillian are combined to show the emergence of the time crystal and to prove the robustness of the oscillation period against quantum fluctuations.

中文翻译：

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有或没有Z ₂对称破坏的耗散时间晶体

我们研究了一种由两种相互作用的驱动耗散玻色子模式组成的新兴半经典时间晶体。该系统具有离散的 $\mathbb Z_2$ 空间对称性，根据驱动的强度，它可以在时间结晶阶段被破坏，也可以不能。精确的半经典平均场分析、量子范围内的数值模拟和 Liouvillian 的光谱分析相结合，以显示时间晶体的出现并证明振荡周期对量子涨落的鲁棒性。