标题： 耗散时间晶体的环面分岔 显示英文标题

标题： Torus bifurcation of a dissipative time crystal

摘要： 使用由横纵泵浦激光强耦合到高精细度光学腔的玻色-爱因斯坦凝聚体组成的量子气体装置，我们实验观察到一个耗散连续时间晶体（CTC）向表现出两个显著振荡频率的时间晶体状态的不稳定性。应用平均场近似模型和弗洛凯分析，我们理论确认该转变是多体系统中极限环（LC）和极限环面（LT）之间环面分岔的表现。我们用最小模型理论说明了LC和LT吸引子，并通过应用塔肯斯嵌入定理到非破坏性测量的腔内光子动力学，实验重建了它们。 显示英文摘要

摘要： Using a quantum gas setup consisting of a Bose-Einstein condensate strongly coupled to a high-finesse optical cavity by a transverse pump laser, we experimentally observe an instability of a dissipative continuous time crystal (CTC) towards a time crystalline state exhibiting two prominent oscillation frequencies. Applying a mean-field approximation model and a Floquet analysis, we theoretically confirm that this transition is a manifestation in a many-body system of a torus bifurcation between a limit cycle (LC) and a limit torus (LT). We theoretically illustrate the LC and LT attractors using the minimal model and experimentally reconstruct them using Takens' embedding theorem applied to the non-destructively measured intracavity photon dynamics.