## Research

__Classical Phase Space Crystals in Open Environment__

It was recently discovered that a crystalline many-body state can exist in the phase space of a closed dynamical system. Phase space crystal can be anomalous Chern insulator that supports chiral topological transport without breaking physical time-reversal symmetry [L. Guo et al., Phys. Rev. B 105, 094301 (2022)]. In this work, we further study the effects of open dissipative environment with thermal noise, and identify the existence condition of classical phase space crystals in realistic scenarios. By defining a crystal order parameter, we plot the phase diagram in the parameter space of dissipation rate, interaction and temperature. Our present work paves the way to realise phase space crystals and explore anomalous chiral transport in experiments.

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__Topological Molecules and Topological Localization of a Rydberg Electron on a Classical Orbit__

It is common knowledge that atoms can form molecules if they attract each other. Here we show that it is possible to create molecules where bound states of atoms are not the result of the attractive interactions but have the topological origin. That is, bound states of atoms correspond to topologically protected edge states of a topological model. Such topological molecules can be realized if the interaction strength between ultra-cold atoms is properly modulated in time. Similar mechanism allows one to realize topologically protected localization of an electron on a classical orbit if a Rydberg atom is perturbed by a properly modulated microwave field.

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__Homogeneous Floquet time crystal from weak ergodicity breaking__

Recent works on observation of discrete time-crystalline signatures throw up major puzzles on the necessity of localization for stabilizing such out-of-equilibrium phases. Motivated by these studies, we delve into a clean interacting Floquet system whose quasi-spectrum conforms to the ergodic Wigner-Dyson distribution, yet with an unexpectedly robust, long-lived time-crystalline order in the absence of fine-tuning or any explicit local constraint. We relate such behavior to a measure zero set of nonthermal Floquet eigenstates with long- range spatial correlations, which coexist with otherwise thermal states at near-infinite temperature and develop a high overlap with a family of translationally invariant, symmetry-broken initial conditions. This resembles the notion of “dynamical scar states” that remain robustly localized throughout a thermalizing Floquet spectrum with fractured structure. We dub such a long-lived discrete time crystal formed in partially nonergodic systems, “scarred discrete time crystal” which is distinct by nature from those stabilized by either many-body localization or prethermalization mechanism.