Realization of a time-crystal in a dc-driven atom-cavity system

这一方案的中心目标是利用原子-腔系统实验实现直流驱动的时间晶体，该系统包括强耦合到高精细低带宽光学腔的玻色-爱因斯坦凝聚体(BEC)。为此，我建议使用到目前为止尚未实验探索的泵浦光区，它相对于相关的原子共振是蓝色失谐的。理论准备工作表明，这一努力取得成功的可能性很大。项目描述中提出的平均场和截断的Wigner模拟预测了一个丰富的相图，它具有四个不同的多体状态：均匀的BEC相、密度波相、时间晶体相和混沌相。在临界泵浦强度以上，原子样品形成一种自组织布拉格光栅，称为密度波相位。这一阶段在泵浦强度的第二阈值以上变得不稳定。由此产生的物质的非平衡态打破了时间平移对称性，实现了时间晶体的概念。到目前为止，所有实现的时间晶体都打破了离散的时间平移对称性，因此被称为弗洛奎时间晶体。这个项目的一个值得注意的新奇之处是创造了一种时间晶体，它打破了连续的时间平移对称性，因此对空间晶体概念进行了更严格的类比。

The central objective of this proposal is to experimentally realize a dc driven time-crystal using an atom-cavity system comprising a Bose-Einstein condensate (BEC) strongly coupled to a high-finesse low-bandwidth optical cavity. To this end, I propose to employ the so far experimentally unexplored regime of pump light, which is blue detuned with respect to the relevant atomic resonances. Theoretical preparatory work indicates excellent chances that this endeavour should succeed. The mean-field and truncated Wigner simulations presented in the project description predict a rich phase diagram with four distinct many-body states: a homogenous BEC phase, a density wave phase, a time-crystal phase and a chaotic phase. Above a critical pump strength, the atomic sample forms a self-organized Bragg grating referred to as density wave phase. This phase becomes unstable above a second threshold value of the pump strength. The resulting non-equilibrium state of matter breaks the time-translation symmetry and realizes the concept of a time-crystal. All so far realized time-crystals break a discrete time-translation symmetry and are therefore called Floquet time-crystals. A notable novelty of this project is the creation of a time-crystal that breaks a continuous time-translation symmetry, such that a more stringent analogy to the concept of spatial crystals holds.