We study the unitary dynamics of randomly or quasiperiodically driven tilted Bose-Hubbard (tBH) model in one dimension deep inside its Mott phase starting from a ${\mathbb{Z}}_2$ symmetry-broken state. The randomness is implemented via a telegraph noise protocol in the drive period while the quasiperiodic drive is chosen to correspond to a Thue-Morse sequence. The periodically driven tBH model (with a square pulse protocol characterized by a time period $T$) is known to exhibit transitions from dynamical regimes with long-time coherent oscillations to those with rapid thermalization. Here we show that starting from a regime where the periodic drive leads to rapid thermalization, a random drive, which consists of a random sequence of square pulses with period $T+\alpha dT$, where $\alpha =\pm 1$ is a random number and $dT$ is the amplitude of the noise, restores long-time coherent oscillations for special values of $dT$. A similar phenomenon can be seen for a quasiperiodic drive following a Thue-Morse sequence where such coherent behavior is shown to occur for a larger number of points in the $(T,dT)$ plane due to the additional structure of the drive protocol. We chart out the dynamics of the system in the presence of such aperiodic drives, provide a qualitative analytical understanding of this phenomenon, point out the role of quantum scars behind it, and discuss experiments which can test our theory.

中文翻译：

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通过多体量子系统中的非周期性驱动恢复相干性

我们研究了随机或准周期驱动的倾斜Bose-Hubbard（tBH）模型在其Mott相深处的一维中的单位动力学，从 ${\mathbb{ž}}_2$对称破坏状态。在驱动周期中通过电报噪声协议实现随机性，同时选择准周期驱动来对应于Thue-Morse序列。周期性驱动的tBH模型（具有以时间段为特征的方波协议）$Ť$已知）会表现出从具有长时间相干振荡的动态状态到具有快速热化的那些状态的过渡。在这里，我们表明，从周期性驱动导致快速热化的状态开始，随机驱动由随机的方波序列和周期组成$Ť+\alpha dŤ$，在哪里 $\alpha =\pm \mathrm{1个}$ 是一个随机数， $dŤ$ 是噪声的幅度，对于特定的值，可以恢复长时间的相干振荡 $dŤ$。对于遵循Thue-Morse序列的准周期驱动器，可以看到类似的现象，其中这种相干行为显示为发生在较大数量的点上。$（Ť，dŤ）$平面由于驱动协议的附加结构。我们在存在这种非周期性驱动的情况下绘制出系统的动力学图，对这种现象提供定性的分析理解，指出其背后的量子疤痕的作用，并讨论可以验证我们理论的实验。