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Study of phase transitions provide insights into how a many-body system behaves under different conditions, enabling us to understand the symmetry breaking, critical phenomena, and topological properties. Strong long-range interactions in highly excited Rydberg atoms create a versatile platform for exploring exotic emergent topological phases. Here, we report the experimental observation of dynamical topological phase transitions in cold Rydberg atomic gases under a microwave field driving. By measuring the system transmission curves while varying the probe intensity, we observe complex hysteresis trajectories characterized by distinct winding numbers as they cross the critical point. At the transition state, where the winding number flips, the topology of these hysteresis trajectories evolves into more non-trivial structures. The topological trajectories are shown to be robust against noise, confirming their rigidity in dynamic conditions. These findings contribute to the insights of emergence of complex dynamical topological phases in many-body systems.

The interactions between Rydberg atoms and microwave fields provide a valuable framework for studying the complex dynamics out of equilibrium, exotic phases, and critical phenomena in many-body physics. This unique interplay allows us to explore various regimes of nonlinearity and phase transitions. Here, we observe a phase transition from the state in the regime of bistability to that in multistability in strongly interacting Rydberg atoms by varying the microwave field intensity, accompanying with the breaking of Z3-symmetry. During the phase transition, the system experiences a hidden critical point, in which the multistable states are difficult to be identified. Through changing the initial state of system, we can identify a hidden multistable state and reveal a hidden trajectory of phase transition, allowing us to track to a hidden critical point. In addition, we observe multiple phase transitions in spectra, suggesting higher-order symmetry breaking. The reported results shed light on manipulating multistability in dissipative Rydberg atoms systems and hold promise in the applications of non-equilibrium many-body physics., Comment: 10 pages, 5 figures

The interplay between strong long-range interactions and the coherent driving contribute to the formation of complex patterns, symmetry, and novel phases of matter in many-body systems. However, long-range interactions may induce an additional dissipation channel, resulting in non-Hermitian many-body dynamics and the emergence of exceptional points in spectrum. Here, we report experimental observation of interaction-induced exceptional points in cold Rydberg atomic gases, revealing the breaking of charge-conjugation parity symmetry. By measuring the transmission spectrum under increasing and decreasing probe intensity, the interaction-induced hysteresis trajectories are observed, which give rise to non-Hermitian dynamics. We record the area enclosed by hysteresis loops and investigate the dynamics of hysteresis loops. The reported exceptional points and hysteresis trajectories in cold Rydberg atomic gases provide valuable insights into the underlying non-Hermitian physics in many-body systems, allowing us to study the interplay between long-range interactions and non-Hermiticity.

Crystal seeding enables a deeper understanding of phase behavior, leading to the development of methods for controlling and manipulating phase transitions in various applications such as materials synthesis, crystallization processes, and phase transformation engineering. How to seed a crystalline in time domain is an open question, which is of great significant and may provide an avenue to understand and control time-dependent quantum many-body physics. Here, we utilize a microwave pulse as a seed to induce the formation of a discrete time crystal in Floquet driven Rydberg atoms. In the experiment, the periodic driving on Rydberg states acts as a seeded crystalline order in subspace, which triggers the time-translation symmetry breaking across the entire ensemble. The behavior of the emergent time crystal is elaborately linked to alterations in the seed, such as the relative phase shift and the frequency difference, which result in phase dependent seeding and corresponding shift in periodicity of the time crystal, leading to embryonic synchronization. This result opens up new possibilities for studying and harnessing time-dependent quantum many-body phenomena, offering insights into the behavior of complex many-body systems under seeding.