驱动BCS系统中的涌现参数共振和时晶相位
Emergent parametric resonances and time-crystal phases in driven BCS systems
摘要：
研究了周期驱动下Bardeen-Cooper-Schrieffer凝聚体的非平衡动力学。我们证明了驱动器和相互作用的综合效果，在新兴的参数共振，类似于一个垂直驱动的钟摆。特别地，当驱动频率与$2Δ_0/n$匹配时，阿诺德舌状物出现，其中$n$是自然数，并且$Δ_0$是平衡间隙参数。在Arnold舌内部，我们发现了一个相称的时间晶体凝聚体，它保留了母超流/超导相的$U(1)$对称性破缺，并显示出额外的时间平移对称性破缺。在这些舌头之外，淬火协议中发现的同步集体希格斯模式是稳定的，而不需要强扰动。我们的结果是直接相关的冷原子和凝聚态系统，并不需要很长的能量弛豫时间来观察。
英文摘要：
We study the out-of-equilibrium dynamics of a Bardeen-Cooper-Schrieffer condensate subject to a periodic drive. We demonstrate that the combined effect of drive and interactions results in emerging parametric resonances, analogous to a vertically driving pendulum. In particular, Arnold tongues appear when the driving frequency matches $2Δ_0/n$, with $n$ a natural number, and $Δ_0$ the equilibrium gap parameter. Inside the Arnold tongues we find a commensurate time-crystal condensate which retains the $U(1)$ symmetry breaking of the parent superfluid/superconducting phase and shows an additional time-translational symmetry breaking. Outside these tongues, the synchronized collective Higgs mode found in quench protocols is stabilized without the need of a strong perturbation. Our results are directly relevant to cold-atom and condensed-matter systems and do not require very long energy relaxation times to be observed.
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