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

本研究的中心目标是利用一个原子腔系统，通过实验实现一个直流驱动的时间晶体，该系统由一个玻色-爱因斯坦凝聚体（BEC）与一个高精细度低带宽光学腔强耦合组成。为此，我建议采用迄今为止实验尚未探索的泵浦光体制，这是相对于相关原子共振的蓝色失谐。理论上的准备工作表明，这一努力极有可能成功。项目描述中提出的平均场和截断Wigner模拟预测了一个具有四种不同多体态的丰富相图：均匀BEC相、密度波相、时间晶体相和混沌相。在临界泵浦强度以上，原子样品形成自组织的布拉格光栅，称为密度波相位。这一阶段在泵强度的第二个阈值以上变得不稳定。由此产生的物质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，所有已实现的时间晶体都打破了离散的时间平移对称，因此被称为Floquet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个时间晶体，打破了连续的时间平移对称，这样就可以更严格地类比空间晶体的概念。

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.