A Moiré time crystal is a non-equilibrium quantum phase emerging from the coherent interference of two distinct frequencies, at least one being the intrinsic oscillation of a symmetry-broken time crystal. Its hallmark is an ultra-long beat period, reflecting a time-domain mapping of the Moiré fringes that arise from mismatched spatial lattices. However, to date, no experimental realization of such a Moiré time crystal has been reported. In this work, by applying a bichromatic driving field with two distinct frequencies, we demonstrate that the interplay between long-range Rydberg interactions and dissipation gives rise to a unique comb-like Moiré pattern characterized by a beat-note comb, which superimposes subharmonic periodicity and fundamental frequencies. This Moiré pattern formed by two mismatched drives is staggered in the spectrum as the frequency of one driver changes. We experimentally map the phase diagram of the system and identify a robust region where the Moiré temporal order persists against perturbations in laser detuning. The reported Moiré time crystal not only provides a controllable platform for exploring emergent slow-fast dynamics and synthetic space-time symmetries but also opens avenues for engineering complex temporal order in driven quantum many-body systems.
A Moiré time crystal is a non-equilibrium quantum phase emerging from the coherent interference of two distinct frequencies, at least one being the intrinsic oscillation of a symmetry-broken time crystal. Its hallmark is an ultra-long beat period, reflecting a time-domain mapping of the Moiré fringes that arise from mismatched spatial lattices. However, to date, no experimental realization of such a Moiré time crystal has been reported. In this work, by applying a bichromatic driving field with two distinct frequencies, we demonstrate that the interplay between long-range Rydberg interactions and dissipation gives rise to a unique comb-like Moiré pattern characterized by a beat-note comb, which superimposes subharmonic periodicity and fundamental frequencies. This Moiré pattern formed by two mismatched drives is staggered in the spectrum as the frequency of one driver changes. We experimentally map the phase diagram of the system and identify a robust region where the Moiré temporal order persists against perturbations in laser detuning. The reported Moiré time crystal not only provides a controllable platform for exploring emergent slow-fast dynamics and synthetic space-time symmetries but also opens avenues for engineering complex temporal order in driven quantum many-body systems.
A time crystal is an exotic phase of matter where time-translational symmetry is broken; this phase differs from the spatial symmetry breaking induced in crystals in space. Lots of experiments report the transition from a thermal equilibrium phase to time crystal phase. However, there is no experimental method to probe the bifurcation effect of distinct time crystals in quantum many-body systems. Here, in a driven and dissipative many-body Rydberg atom system, we observe multiple continuous dissipative time crystals and emergence of more complex temporal symmetries beyond the single time crystal phase. Bifurcation of time crystals in strongly interacting Rydberg atoms is observed; the process manifests as a transition from a time crystal state of long temporal order to one of short temporal order, or vice versa. By manipulating the driving field parameters, we observe the time crystal's bistability and a hysteresis loop. These investigations indicate new possibilities for control and manipulation of the temporal symmetries of non-equilibrium systems.
Discrete time quasicrystals (DTQC) constitute a class of non-equilibrium matter characterized by temporal order without strict periodicity, in contrast to conventional time crystals. Investigating these phenomena is essential for expanding our fundamental understanding of far-from-equilibrium quantum matter and spontaneous symmetry breaking beyond periodic regimes. Here, we experimentally observe a DTQC in a driven-dissipative ensemble of strongly interacting Rydberg atoms, displaying non-equilibrium dynamical response with a different finite Abelian group symmetry Zm×Zn. By applying a quasiperiodic drive using a dual-frequency drive with incommensurate frequencies, we demonstrate that the system exhibits a robust subharmonic response at multiple incommensurate frequencies, signifying the emergence of a DTQC phase. We map the full phase diagram of the system, which includes the DTQC phase, and demonstrate its rigidity against perturbations in both RF field intensity and laser detuning. Moreover, we observe a cyclic group symmetry effect that constrains the construction of Z2×Z3-symmetric DTQC. This work establishes a versatile platform for studying non-equilibrium phases of matter and provides insights into the dynamics of time-translation symmetry breaking in quantum many-body systems. Time-crystal phases have raised both theoretical and experimental interest across various platforms. Here, the authors report the observation of a discrete time-quasicrystal in a driven-dissipative ensemble of interacting Rydberg atoms, advancing the understanding of symmetry breaking in these systems.
Driven nonlinear oscillators constitute a universal paradigm for understanding synchronization, frequency pulling, and frequency comb formation in nonequilibrium systems. Here, we realize such an emergent nonlinear oscillator in strongly interacting cesium Rydberg vapor, where coherent optical excitation, dissipation, and long-range interactions give rise to a driven-dissipative time crystal phase with intrinsic oscillation frequencies. Applying a radio-frequency (RF) field allows controlled tuning of the intrinsic oscillation frequency. Under RF heterodyne conditions, we observe intermodulation, frequency pulling, and, at strong drive, the emergence of a comb-like spectrum in the atomic coherence. We quantitatively capture these observations using a four-level mean-field model and demonstrate a classical analogue with a driven Van der Pol oscillator. Our results establish interacting Rydberg ensembles as a tunable platform for exploring nonequilibrium time-crystalline order, nonlinear synchronization, and frequency comb generation in many-body atomic systems.
A time crystal is an exotic phase of matter where time-translational symmetry is broken; this phase differs from the spatial symmetry breaking induced in conventional crystals. Lots of experiments report the transition from a thermal equilibrium phase to a time crystal phase. However, there is no experimental method to probe the bifurcation effect of distinct continuous time crystals in quantum many-body systems. Here, in a driven and dissipative many-body Rydberg atom system, we observe multiple continuous dissipative time crystals and emergence of more complex temporal symmetries beyond the single time crystal phase. Bifurcation of time crystals in strongly interacting Rydberg atoms is observed; the process manifests as a transition from a time crystal of long periodicity to a time crystal of short periodicity, or vice versa. By manipulating the driving field parameters, we observe the time crystal’s bistability and a hysteresis loop. These investigations indicate new possibilities for control and manipulation of the temporal symmetries of non-equilibrium systems. The time crystal is an exotic phase of matter where time-translational symmetry is broken. Here, the authors observe multiple continuous dissipative time crystals and bifurcation of time crystals in driven and dissipative Rydberg atomic gas.
Non-equilibrium Rydberg gases exhibit exotic many-body phases stabilized by the interplay of coherent interactions and dissipation. Strong Rydberg interactions drive sustained limit cycle oscillations, whose robustness, long-range temporal order, and spontaneous time-translation symmetry breaking establish a dissipative time crystal (DTC). Collective self-entrainment in driven ensembles leads to global synchronization and a dominant oscillation frequency. Here, injection locking of a Rydberg DTC is demonstrated using a radio-frequency (RF) electric field that gradually pulls the intrinsic oscillation toward the injected frequency. Above a critical threshold, full synchronization occurs, with the locking bandwidth scaling linearly with RF amplitude. This includes synchronization of higher-order harmonics, revealing entrainment of the system’s nonlinear temporal dynamics. The phenomenon parallels injection locking in classical nonlinear systems, but emerges here in a strongly interacting quantum medium. This approach establishes a new method for stabilizing and controlling time-crystalline temporal order, with applications in precision sensing, quantum metrology, and timekeeping. Non-equilibrium Rydberg gases exhibit unique many-body phases arising from the interplay of coherent interactions and dissipation, yet controlling their temporal order remains challenging. This work demonstrates injection locking of a Rydberg dissipative time crystal using a radio-frequency electric field, achieving full synchronization and revealing dynamical behavior relevant to precision sensing and quantum metrology.
Abstract The discovery of time crystals and topological phases has fundamentally altered our understanding of quantum matter, yet a unified framework that combines temporal quasi-order, topological protection, and engineered dissipation remains a central challenge. Here we introduce Floquet-engineered dissipative time quasicrystals (FDTCs) —a class of nonequilibrium topological phases that emerge from the synergy of quasi-periodic driving, non-local dissipation, and non-Hermitian topology. Using a combination of Floquet-Lindblad theory and frequency-space topology, we demonstrate that FDTCs exhibit three defining hallmarks: (i) fractal temporal correlations with multiple incommensurate frequencies, (ii) a quantized topological invariant robust against disorder, and (iii) algebraically decaying memory of phase perturbations—a signature of intrinsic protection. We establish a general theoretical framework mapping quasi-periodically driven dissipative systems to non-Hermitian tight-binding models on synthetic frequency lattices, revealing topological edge modes in the frequency domain that manifest as persistent temporal order. We provide explicit experimental blueprints for two leading quantum platforms: parametrically driven superconducting qubit arrays and Rydberg atom chains with structured dissipation. Numerical simulations validate the phase diagram, showing that FDTCs occupy a distinct region bounded by trivial dissipative dynamics, conventional time crystals, and thermal phases. Our work establishes FDTCs as a bridge between topological matter, non-equilibrium physics, and quantum simulation, opening pathways to dissipationprotected quantum memory, topologically robust frequency combs, and novel non-Hermitian quantum technologies.