Dissipative Prethermal Discrete Time Crystal

Bifurcation of time crystals in driven and dissipative Rydberg atomic gas

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.

Emergent symmetries in prethermal phases of periodically driven quantum systems

Periodically driven closed quantum systems are expected to eventually heat up to infinite temperature; reaching a steady state described by a circular orthogonal ensemble. However, such finite driven systems may exhibit sufficiently long prethermal regimes; their properties in these regimes are qualitatively different from that of their corresponding infinite temperature steady states. These, often experimentally relevant, prethermal regimes host a wide range of phenomena; they may exhibit dynamical localization and freezing, host Floquet scars, display signatures of Hilbert space fragmentation, and exhibit time crystalline phases. Such phenomena are often accompanied by emergent approximate dynamical symmetries which have no analogue in equilibrium systems. In this review, we provide a pedagogical introduction to the origin and nature of these symmetries and discuss their role in shaping the prethermal phases of a class of periodically driven closed quantum systems.

Theory for Dissipative Time Crystals in Coupled Parametric Oscillators

Discrete time crystals are novel phases of matter that break the discrete time translational symmetry of a periodically driven system. In this Letter, we propose a classical system of weakly nonlinear parametrically driven coupled oscillators as a test bed to understand these phases. Such a system of parametric oscillators can be used to model period-doubling instabilities of Josephson junction arrays as well as semiconductor lasers. To show that this instability leads to a discrete time crystal we first show that a certain limit of the system is close to Langevin dynamics in a symmetry breaking potential. We numerically show that this phase exists even in the presence of Ising symmetry breaking using a Glauber dynamics approximation. We then use a field theoretic argument to show that these results are robust to other approximations including the semiclassical limit when applied to dissipative quantum systems.

Higher-order and fractional discrete time crystals in Floquet-driven Rydberg atoms

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.

Applicability of Mean-Field Theory for Time-Dependent Open Quantum Systems with Infinite-Range Interactions

Understanding quantum many-body systems with long-range or infinite-range interactions is of relevance across a broad set of physical disciplines, including quantum optics, nuclear magnetic resonance, and nuclear physics. From a theoretical viewpoint, these systems are appealing since they can be efficiently studied with numerics, and in the thermodynamic limit are expected to be governed by mean-field equations of motion. Over the past years the capabilities to experimentally create long-range interacting systems have dramatically improved permitting their control in space and time. This allows us to induce and explore a plethora of nonequilibrium dynamical phases, including time crystals and even chaotic regimes. However, establishing the emergence of these phases from numerical simulations turns out to be surprisingly challenging. This difficulty led to the assertion that mean-field theory may not be applicable to time-dependent infinite-range interacting systems. Here, we rigorously prove that mean-field theory in fact exactly captures their dynamics, in the thermodynamic limit. We further provide bounds for finite-size effects and their dependence on the evolution time.

Stable Measurement-Induced Floquet Enriched Topological Order

The Floquet code utilizes a periodic sequence of two-qubit measurements to realize the topological order. After each measurement round, the instantaneous stabilizer group can be mapped to a honeycomb toric code, explaining the topological feature. The code also possesses a time-crystal order-the e-m transmutation after every cycle, breaking the Floquet symmetry of the measurement schedule. This behavior is distinct from the stationary topological order realized in either random circuits or time-independent Hamiltonian. Therefore, the resultant phase belongs to the overlap between the classes of Floquet enriched topological orders and measurement-induced phases. In this Letter, we construct a continuous path interpolating between the Floquet and toric codes, focusing on the transition between the time-crystal and stationary topological phases. We show that this transition is characterized by a divergent length scale. We also add single-qubit perturbations to the model and obtain a richer two-dimensional parametric phase diagram of the Floquet code, showing the stability of the Floquet enriched topological order.