标题： 观察从连续时间晶体到离散时间晶体的相变 显示英文标题

标题： Observation of a phase transition from a continuous to a discrete time crystal

摘要： 离散时间晶体（DTCs）和连续时间晶体（CTCs）是新型的动态多体状态，其特征是具有鲁棒性的自持振荡，通过离散或连续时间平移对称性的自发破缺而出现。 DTCs 是周期性驱动的系统，以外部驱动的次谐波振荡，而 CTCs 是连续驱动的，并以系统固有的频率振荡。 在这里，我们探索从连续时间晶体到离散时间晶体的相变。 在一个连续泵浦的原子-腔系统中制备一个具有特征振荡频率$\omega_\mathrm{CTC}$的 CTC。 用接近$2\,\omega_\mathrm{CTC}$的频率$\omega_{\mathrm{dr}}$调制 CTC 的泵浦强度，会导致$\omega_\mathrm{CTC}$与$\omega_{\mathrm{dr}}/2$强烈锁定，从而产生 DTC。 这种量子多体系统中的相变与非线性机械和电子振荡器或激光器的次谐波注入锁定有关。 显示英文摘要

摘要： Discrete (DTCs) and continuous time crystals (CTCs) are novel dynamical many-body states, that are characterized by robust self-sustained oscillations, emerging via spontaneous breaking of discrete or continuous time translation symmetry. DTCs are periodically driven systems that oscillate with a subharmonic of the external drive, while CTCs are continuously driven and oscillate with a frequency intrinsic to the system. Here, we explore a phase transition from a continuous time crystal to a discrete time crystal. A CTC with a characteristic oscillation frequency $\omega_\mathrm{CTC}$ is prepared in a continuously pumped atom-cavity system. Modulating the pump intensity of the CTC with a frequency $\omega_{\mathrm{dr}}$ close to $2\,\omega_\mathrm{CTC}$ leads to robust locking of $\omega_\mathrm{CTC}$ to $\omega_{\mathrm{dr}}/2$, and hence a DTC arises. This phase transition in a quantum many-body system is related to subharmonic injection locking of non-linear mechanical and electronic oscillators or lasers.