The two main research questions on time crystals are: What is a time crystal? Is there a material that is spontaneously crystalline in time? This study synthesizes a photonic material of topological Floquet time crystals and experimentally observes its indicative period‐ beating. A single‐particle picture is explicitly reconstructed of discrete time‐crystalline phase and is revealed using an appropriately‐designed photonic Floquet simulator the rigid period‐doubling as a signature of the breakage of the discrete time‐translational symmetry. Unlike the requirement of the many‐body localization, the photonic Floquet time crystal is derived from a newly defined single‐particle topological phase that can be extensively accessed by many pertinent nonequilibrium and periodically‐driven platforms. The observation will drive theoretical and technological interests toward condensed matter physics and topological photonics.
The two main research questions on time crystals are: What is a time crystal? Is there a material that is spontaneously crystalline in time? This study synthesizes a photonic material of topological Floquet time crystals and experimentally observes its indicative period‐ beating. A single‐particle picture is explicitly reconstructed of discrete time‐crystalline phase and is revealed using an appropriately‐designed photonic Floquet simulator the rigid period‐doubling as a signature of the breakage of the discrete time‐translational symmetry. Unlike the requirement of the many‐body localization, the photonic Floquet time crystal is derived from a newly defined single‐particle topological phase that can be extensively accessed by many pertinent nonequilibrium and periodically‐driven platforms. The observation will drive theoretical and technological interests toward condensed matter physics and topological photonics.
Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry. The period of the resulting discrete time crystal is quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization. Here, we consider a simple model for a one-dimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied. We numerically map out its phase diagram and compute the properties of the dynamical phase transition where the time crystal melts into a trivial Floquet insulator. Moreover, we demonstrate that the model can be realized with current experimental technologies and propose a blueprint based upon a one dimensional chain of trapped ions. Using experimental parameters (featuring long-range interactions), we identify the phase boundaries of the ion-time-crystal and propose a measurable signature of the symmetry breaking phase transition.
Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry.The period of the resulting discrete time crystal is quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization.Here, we consider a simple model for a onedimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied.We numerically map out its phase diagram and compute the properties of the dynamical phase transition where the time crystal melts into a trivial Floquet insulator.Moreover, we demonstrate that the model can be realized with current experimental technologies and propose a blueprint based upon a one dimensional chain of trapped ions.Using experimental parameters (featuring long-range interactions), we identify the phase boundaries of the ion-time-crystal and propose a measurable signature of the symmetry breaking phase transition.
Time crystals are physical systems whose time translation symmetry is spontaneously broken. Although the spontaneous breaking of continuous time-translation symmetry in static systems is proved impossible for the equilibrium state, the discrete time-translation symmetry in periodically driven (Floquet) systems is allowed to be spontaneously broken, resulting in the so-called Floquet or discrete time crystals. While most works so far searching for time crystals focus on the symmetry breaking process and the possible stabilising mechanisms, the many-body physics from the interplay of symmetry-broken states, which we call the condensed matter physics in time crystals, is not fully explored yet. This review aims to summarise the very preliminary results in this new research field with an analogous structure of condensed matter theory in solids. The whole theory is built on a hidden symmetry in time crystals, i.e., the phase space lattice symmetry, which allows us to develop the band theory, topology and strongly correlated models in phase space lattice. In the end, we outline the possible topics and directions for the future research.
The engineering of new states of matter through Floquet driving has revolutionized the field of condensed matter physics. This technique enables the creation of hybrid topological states and ordered phases that are absent in normal systems. Crystalline structures, exemplifying spatially ordered systems under periodic driving, have been extensively studied. However, recent focus has shifted towards discrete time crystals (DTCs), periodically driven quantum many-body systems that break time translation symmetry under specific conditions. In this paper, the model of discrete time crystals is extended to allow for the formation of time-varying tesseracts, allowing for the investigation of time translational symmetry in pseudo-higher-dimensional lattice systems.
Abstract Time crystals are physical systems whose time translation symmetry is spontaneously broken. Although the spontaneous breaking of continuous time-translation symmetry in static systems is proved impossible for the equilibrium state, the discrete time-translation symmetry in periodically driven (Floquet) systems is allowed to be spontaneously broken, resulting in the so-called Floquet or discrete time crystals. While most works so far searching for time crystals focus on the symmetry breaking process and the possible stabilising mechanisms, the many-body physics from the interplay of symmetry-broken states, which we call the condensed matter physics in time crystals, is not fully explored yet. This review aims to summarise the very preliminary results in this new research field with an analogous structure of condensed matter theory in solids. The whole theory is built on a hidden symmetry in time crystals, i.e., the phase space lattice symmetry, which allows us to develop the band theory, topology and strongly correlated models in phase space lattice. In the end, we outline the possible topics and directions for the future research.
Time crystals form when arbitrary physical states of a periodically driven system spontaneously break discrete time-translation symmetry. We introduce one-dimensional time-crystalline topological superconductors, for which time-translation symmetry breaking and topological physics intertwine-yielding anomalous Floquet Majorana modes that are not possible in free-fermion systems. Such a phase exhibits a bulk magnetization that returns to its original form after two drive periods, together with Majorana end modes that recover their initial form only after four drive periods. We propose experimental implementations and detection schemes for this new state.