01851nas a2200169 4500008004100000245006100041210006000102260001400162520134300176100002501519700001901544700002401563700001801587700001901605700002001624856003701644 2023 eng d00aColloquium: Quantum and Classical Discrete Time Crystals0 aColloquium Quantum and Classical Discrete Time Crystals c5/15/20233 a

The spontaneous breaking of time translation symmetry has led to the discovery of a new phase of matter - the discrete time crystal. Discrete time crystals exhibit rigid subharmonic oscillations, which result from a combination of many-body interactions, collective synchronization, and ergodicity breaking. This Colloquium reviews recent theoretical and experimental advances in the study of quantum and classical discrete time crystals. We focus on the breaking of ergodicity as the key to discrete time crystals and the delaying of ergodicity as the source of numerous phenomena that share many of the properties of discrete time crystals, including the AC Josephson effect, coupled map lattices, and Faraday waves. Theoretically, there exists a diverse array of strategies to stabilize time crystalline order in both closed and open systems, ranging from localization and prethermalization to dissipation and error correction. Experimentally, many-body quantum simulators provide a natural platform for investigating signatures of time crystalline order; recent work utilizing trapped ions, solid-state spin systems, and superconducting qubits will be reviewed. Finally, this Colloquium concludes by describing outstanding challenges in the field and a vision for new directions on both the experimental and theoretical fronts.

1 aZaletel, Michael, P.1 aLukin, Mikhail1 aMonroe, Christopher1 aNayak, Chetan1 aWilczek, Frank1 aYao, Norman, Y. uhttps://arxiv.org/abs/2305.0890401981nas a2200241 4500008004100000245005400041210005400095260001300149520129500162100002501457700002301482700002001505700002001525700002201545700002201567700001401589700001901603700001801622700001801640700002001658700002401678856003701702 2021 eng d00aObservation of a prethermal discrete time crystal0 aObservation of a prethermal discrete time crystal c2/2/20213 a

The conventional framework for defining and understanding phases of matter requires thermodynamic equilibrium. Extensions to non-equilibrium systems have led to surprising insights into the nature of many-body thermalization and the discovery of novel phases of matter, often catalyzed by driving the system periodically. The inherent heating from such Floquet drives can be tempered by including strong disorder in the system, but this can also mask the generality of non-equilibrium phases. In this work, we utilize a trapped-ion quantum simulator to observe signatures of a non-equilibrium driven phase without disorder: the prethermal discrete time crystal (PDTC). Here, many-body heating is suppressed not by disorder-induced many-body localization, but instead via high-frequency driving, leading to an expansive time window where non-equilibrium phases can emerge. We observe a number of key features that distinguish the PDTC from its many-body-localized disordered counterpart, such as the drive-frequency control of its lifetime and the dependence of time-crystalline order on the energy density of the initial state. Floquet prethermalization is thus presented as a general strategy for creating, stabilizing and studying intrinsically out-of-equilibrium phases of matter.

1 aKyprianidis, Antonis1 aMachado, Francisco1 aMorong, William1 aBecker, Patrick1 aCollins, Kate, S.1 aElse, Dominic, V.1 aFeng, Lei1 aHess, Paul, W.1 aNayak, Chetan1 aPagano, Guido1 aYao, Norman, Y.1 aMonroe, Christopher uhttps://arxiv.org/abs/2102.0169501563nas a2200169 4500008004100000245002700041210002700068260001400095300001200109490000700121520114400128100002201272700002401294700001801318700002001336856003701356 2020 eng d00aDiscrete Time Crystals0 aDiscrete Time Crystals c3/10/2020 a467-4990 v113 a

Experimental advances have allowed for the exploration of nearly isolated quantum many-body systems whose coupling to an external bath is very weak. A particularly interesting class of such systems is those which do not thermalize under their own isolated quantum dynamics. In this review, we highlight the possibility for such systems to exhibit new non-equilibrium phases of matter. In particular, we focus on "discrete time crystals", which are many-body phases of matter characterized by a spontaneously broken discrete time translation symmetry. We give a definition of discrete time crystals from several points of view, emphasizing that they are a non-equilibrium phenomenon, which is stabilized by many-body interactions, with no analog in non-interacting systems. We explain the theory behind several proposed models of discrete time crystals, and compare a number of recent realizations, in different experimental contexts. 

1 aElse, Dominic, V.1 aMonroe, Christopher1 aNayak, Chetan1 aYao, Norman, Y. uhttps://arxiv.org/abs/1905.13232