Nonequilibrium, strongly interacting systems exhibit rich dynamics even in the presence of strong dissipation. For example, periodic dynamics, such as discrete time crystalline (DTC) phases, can appear. The DTC phase structure can be further enriched using external periodic driving-Floquet driving. In this Letter, we study a photoionization-induced Floquet driving of a DTC phase in a thermal Rydberg gas. We add an additional laser to induce photoelectrons from the cell wall. These electrons are rotated around the magnetic-field vector and collide with the Rydberg atoms, generating a plasma with large electric fields that perturb further Rydberg excitation. This results in a photoionization-induced Floquet driving of the DTC phase. Importantly, we demonstrate experimentally how the DTC phase relies on the emergence of bistability. Simulations of the mean-field Floquet-driven system reproduce the experimental observations. Our Letter fills an experimental gap in our understanding of the relation of multistability and dissipative discrete time crystals, and in this regard, it constitutes a highly controlled platform for exploring exotic nonequilibrium physics in dissipative interacting systems.
Nonequilibrium, strongly interacting systems exhibit rich dynamics even in the presence of strong dissipation. For example, periodic dynamics, such as discrete time crystalline (DTC) phases, can appear. The DTC phase structure can be further enriched using external periodic driving-Floquet driving. In this Letter, we study a photoionization-induced Floquet driving of a DTC phase in a thermal Rydberg gas. We add an additional laser to induce photoelectrons from the cell wall. These electrons are rotated around the magnetic-field vector and collide with the Rydberg atoms, generating a plasma with large electric fields that perturb further Rydberg excitation. This results in a photoionization-induced Floquet driving of the DTC phase. Importantly, we demonstrate experimentally how the DTC phase relies on the emergence of bistability. Simulations of the mean-field Floquet-driven system reproduce the experimental observations. Our Letter fills an experimental gap in our understanding of the relation of multistability and dissipative discrete time crystals, and in this regard, it constitutes a highly controlled platform for exploring exotic nonequilibrium physics in dissipative interacting systems.
Higher-order and fractional discrete time crystals (DTCs) are exotic phases of matter where the discrete time translation symmetry is broken into higher-order and non-integer category. Generation of these unique DTCs has been widely studied theoretically in different systems. However, no current experimental methods can probe these higher-order and fractional DTCs in any quantum many-body systems. We demonstrate an experimental approach to observe higher-order and fractional DTCs in Floquet-driven Rydberg atomic gases. We have discovered multiple n-DTCs with integer values of n = 2, 3, and 4, and others ranging up to 14, along with fractional n-DTCs with n values beyond the integers. The system response can transition between adjacent integer DTCs, during which the fractional DTCs are investigated. Study of higher-order and fractional DTCs expands fundamental knowledge of non-equilibrium dynamics and is promising for discovery of more complex temporal symmetries beyond the single discrete time translation symmetry. Discrete-time crystal (DTC) is a special phase of matter that exhibits a spontaneous breaking of the discrete time translational symmetry. Here, Bang Liu et al. demonstrate an experimental approach to observe higher-order and fractional DTCs in Floquet-driven Rydberg atomic gases.
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.
Motivated by experimental observations of time-symmetry breaking behavior in a periodically driven (Floquet) system, we study a one-dimensional spin model to explore the stability of such Floquet discrete time crystals (DTCs) under the interplay between interaction and the microwave driving. For intermediate interactions and high drivings, from the time evolution of both stroboscopic spin polarization and mutual information between two ends, we show that Floquet DTCs can exist in a prethermal time regime without the tuning of strong disorder. For much weak interactions the system is a symmetry-unbroken phase, while for strong interactions it gives its way to a thermal phase. Through analyzing the entanglement dynamics, we show that large driving fields protect the prethermal DTCs from many-body localization and thermalization. Our results suggest that by increasing the spin interaction, one can drive the experimental system into optimal regime for observing a robust prethermal DTC phase.
We investigate the dynamical phases that emerge in collective spin models subjected to a spatially non-uniform periodic drive. Taking the paradigmatic Lipkin-Meshkov-Glick (LMG) model as a concrete platform, we establish that a rich landscape of dynamical phases emerges when two regions of the system are driven with different field strengths, h1 and h2. Remarkably, despite the `all-to-all' nature of the interactions, the system can be driven into dynamical phases characterized by distinct kinds of discrete time crystal (DTC) orders in different parts of the system. Apart from these coexisting DTCs, tuning the driving field leads to the emergence of phases where DTCs coexist with Floquet-synchronized or oscillatory phases; the former has been dubbed a chimera DTC. Finally, we demonstrate that a tunable set of global DTC phases emerges when h1 and h2 are proximate. Crucially, these dynamical regimes can be observed both for experimentally relevant finite-size systems and in the thermodynamic limit. Our results establish spatially structured driving as a powerful route to realize non-equilibrium phase coexistence in collective spin systems.
A discrete time crystal (DTC) is an essentially nonequilibrium phase that breaks discrete time-translation symmetry in periodically driven (Floquet) systems.In ideal isolated quantum systems without dissipation, many kinds of DTCs have been theoretically proposed and experimentally verified in various artificial quantum systems, such as trapped ions, NV centers in diamond, and quantum computers.However, in real physical systems, we cannot avoid dissipation stemming from coupling to an external environment.Nevertheless, the effects of dissipation on DTCs have not been fully explored yet.This thesis reports the author's two original studies on dissipative DTCs.First, we formulate a symmetry-based theory of dissipative DTCs.To this end, we introduce Floquet dynamical symmetry (FDS) governing the long-time dynamics of dissipative Floquet systems.The FDS protects the quantum coherence of the system from dissipation and dephasing and leads to two types of time crystals: the discrete time crystal (DTC) and discrete time quasicrystal (DTQC), which are different in periodicity.We show that these time crystals appear in spin-S Bose-and Fermi-Hubbard models driven by an ac field and that their periodicity can be tuned by adjusting the field strength.Since these time crystals rely on the FDS alone, they appear even in the presence of perturbations as long as the FDS exists.We also elucidate that the FDS explains the symmetry structure behind the conventional DTCs proposed in the previous studies.Second, we investigate dissipative DTCs in solid-state materials by considering a dissipative quantum Ising model periodically driven by π-pulses.While the previous studies on dissipative DTCs have focused on well-controllable artificial quantum systems, we show that realistic dissipation in solids does not destroy but can stabilize the DTC order.Using the time-dependent mean-field theory, we analyze the DTC phase transition and determine critical exponents, including a dynamical one.We also find a novel reentrant phase transition in varying the pulse interval.This transition is due to a nontrivial interplay of the periodic drive and dissipation and has no equilibrium counterparts in the corresponding undriven system.Furthermore, to demonstrate the rigidity (stability) of the DTC, we consider imperfect πpulses, showing that the DTC is robust against minor imperfections and finding that DTQC appears for major imperfections.These results uncover a general symmetry aspect of dissipative DTCs and lay the foundation for realizing DTCs in material science.