We investigate a space-time crystal in a superfluid Bose gas. Using a well-controlled periodic drive we excite only one crystalline mode in the system, which can be accurately modeled in the rotating frame of the drive. Using holographic imaging we observe the stability of the crystal over an extended period of time and show the robustness of its structure in both space and time. By introducing a fourth-order term in the Hamiltonian we show that the crystal stabilizes at a fixed number of quanta. The results of the model are compared to the experimental data and show good agreement, with a small number of free parameters. The results yield insights in the long-term stability of the crystal, which can only be obtained by the combination of the extended control in the experiment and the nearly ab-initio character of the model. From the model we derive a phase diagram of the system, which can be exploited in the future to study the phase transitions for this new state of matter in even more detail.

中文翻译：

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关于时空晶体的长期稳定性

我们研究了超流体玻色气体中的时空晶体。使用控制良好的周期性驱动器，我们只激发系统中的一种晶体模式，可以在驱动器的旋转框架中精确建模。使用全息成像，我们观察晶体在很长一段时间内的稳定性，并显示其结构在空间和时间上的稳健性。通过在哈密顿量中引入四阶项，我们表明晶体稳定在固定数量的量子上。该模型的结果与实验数据进行了比较，显示出良好的一致性，具有少量的自由参数。结果对晶体的长期稳定性产生了见解，这只能通过将实验中的扩展控制和模型的近乎 ab-initio 特征相结合来获得。