Discrete Time Crystals (1905.13232v1)

Abstract: 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.

• The paper introduces discrete time crystals as phases exhibiting spontaneous time-translation symmetry breaking in periodically driven quantum systems.
• It demonstrates numerical results showing stroboscopic robustness and subharmonic oscillations, confirming the stability of these non-equilibrium phases.
• The work outlines experimental and theoretical implications, paving the way for advancements in quantum metrology and computation.

Overview of the Paper "Discrete Time Crystals"

In the paper "Discrete Time Crystals," the authors present an overview of recent advances in the paper of non-equilibrium phases of matter, particularly focusing on discrete time crystals (DTCs). This paper discusses various theoretical frameworks and experimental realizations that reveal DTCs as a novel class of phases characterized by spontaneously broken time-translation symmetry in periodically driven quantum systems.

The concept of a time crystal was initially introduced as a system that breaks continuous time-translation symmetry, akin to how spatial crystals break translational symmetry in space. The paper challenges this notion by focusing on discrete time crystals, which emerge in Floquet systems under periodic driving. Here, the symmetry of time translation is discrete, and the authors emphasize that these time crystals break the period of the drive to yield longer-period responses, such as subharmonic oscillations.

Numerical Results and Claims

The paper presents several strong numerical results supporting the existence of discrete time crystals:

1. Stroboscopic Robustness: By conducting stroboscopic measurements, the researchers observed that local observables in certain quantum systems display dynamics that are periodic with a period that is an integer multiple of the drive's period. This subharmonic response is the haLLMark of a DTC.
2. Spontaneous Symmetry Breaking: The authors assert that DTCs exhibit spontaneous breaking of time-translation symmetry, resulting in long-range temporal order. They provide a detailed theoretical framework grounded in Floquet theory to characterize such broken symmetries.
3. Robustness against Perturbations: A strong claim made is regarding the robustness of these time crystals under perturbations—a property that underscores their stability akin to traditional phases of matter. Various models of DTCs demonstrate resilience to changes in system parameters, provided these are compliant with the discrete time translational symmetry.

Implications and Future Research Directions

This work has both practical and theoretical implications. Practically, realizing DTCs in experimental setups can lead to advancements in quantum metrology and information processing, leveraging the long coherence times associated with the non-equilibrium steady states of time crystals. Theoretically, it opens new frontiers in understanding quantum phases of matter that defy equilibrium descriptions, offering insights into dynamic many-body systems where interactions can lead to stable, non-equilibrium phases.

The research invites further exploration into:

• Explicit Models: Detailed studies of the underlying Hamiltonians that give rise to DTCs, allowing for a clearer classification of these novel phases.
• Experimental Realizations: Efforts to produce and detect DTC behavior in various systems, such as trapped ions, superconducting circuits, and other platforms where quantum coherence and control are paramount.
• Expanding the Framework: Extending the ideas beyond periodic driving to quasi-periodic or other complex drives, which might reveal even richer non-equilibrium phenomena.

In conclusion, the paper "Discrete Time Crystals" elucidates the theoretical underpinnings and potential applications of these fascinating systems, contributing a pivotal step towards understanding anomalies in time-translational symmetry in quantum dynamics. The future exploration of DTCs holds promise for advancing both fundamental physics and the development of robust quantum technologies.