论文标题
一维浮光拓扑绝缘子中的时间晶体阶段的普遍存在和周期倍增的振荡
Universal presence of time-crystalline phases and period-doubling oscillations in one-dimensional Floquet topological insulators
论文作者
论文摘要
在这项工作中，我们报道了一维定期驱动的系统中无处不在的拓扑浮标时间晶体（TFTC）。自发离散时间翻译对称性（DTS）破裂的刚性和实现需要对异常拓扑不变性（0模式和$π$模式）共存，而不是存在障碍或多种物体定位。我们发现，在基础驱动器的特定频率范围内，零和PI模式之间的异常浮子相共存可以产生自发破坏的周期倍加倍（2t，两个驱动器的两个循环），从而导致次谐波响应（$ω/2 $，一半驱动频率）。刚性周期振荡是拓扑周围的，因为在胶质谱中的0和$π$ - gap的非试图打开，因此可以将其视为特定的“ rabi振荡”，并将其视为具有某些quasienergy spplating $π/t $π/t $。我们对时间结晶“基态”的建模可以在实验平台（例如拓扑光子学和超低场）中很容易实现。同样，我们的工作可以带来重大的兴趣，以探索浮雕系统中的拓扑相变，并弥合浮雕拓扑绝缘子和光子学之间的差距，以及时期的时间晶体。
In this work, we reported a ubiquitous presence of topological Floquet time crystal (TFTC) in one-dimensional periodically-driven systems. The rigidity and realization of spontaneous discrete time-translation symmetry (DTS) breaking in our model require necessarily coexistence of anomalous topological invariants (0 modes and $π$ modes), instead of the presence of disorders or many-body localization. We found that in a particular frequency range of the underlying drive, the anomalous Floquet phase coexistence between zero and pi modes can produce the period-doubling (2T, two cycles of the drive) that breaks the spontaneously, leading to the subharmonic response ($ω/2$, half the drive frequency). The rigid period-oscillation is topologically-protected against perturbations due to both non-trivially opening of 0 and $π$-gaps in the quasienergy spectrum, thus, as a result, can be viewed as a specific "Rabi oscillation" between two Floquet eigenstates with certain quasienergy splitting $π/T$. Our modeling of the time-crystalline 'ground state' can be easily realized in experimental platforms such as topological photonics and ultracold fields. Also, our work can bring significant interests to explore topological phase transition in Floquet systems and to bridge the gap between Floquet topological insulators and photonics, and period-doubled time crystals.
