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Science

Prethermal time crystal

Ian S. Osborne

Published Jun 10, 2021• 0 citations
Publisher

Abstract

Quantum Simulation Characterizing and understanding different phases of matter in equilibrium is usually associated with the process of thermalization, where the system equilibrates. Recent efforts probing nonequilibrium systems have revealed that periodic driving of the system can suppress the natural tendency for equilibration yet still form new, nonequilibrium phases. Kyprianidis et al. used a quantum simulator composed of 25 trapped ion qubits and spins to observe such a nonequilibrium phase of matter: the disorder-free prethermal discrete time crystal. The flexibility and tunability of their quantum simulator provide a powerful platform with which to study the exotic phases of matter. Science , abg8102, this issue p. [1192][1] [1]: /lookup/doi/10.1126/science.abg8102

DOI
10.1126/science.372.6547.1162-n

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Quantum Simulation
Characterizing and understanding different phases of matter in equilibrium is usually associated with the process of thermalization, where the system equilibrates. Recent efforts probing nonequilibrium systems have revealed that periodic driving of the system can suppress the natural tendency for equilibration yet still form new, nonequilibrium phases. Kyprianidis et al. used a quantum simulator composed of 25 trapped ion qubits and spins to observe such a nonequilibrium phase of matter: the disorder-free prethermal discrete time crystal. The flexibility and tunability of their quantum simulator provide a powerful platform with which to study the exotic phases of matter.
Science , abg8102, this issue p. 1192
Extending the framework of statistical physics to the nonequilibrium setting has led to the discovery of previously unidentified phases of matter, often catalyzed by periodic driving. However, preventing the runaway heating that is associated with driving a strongly interacting quantum system remains a challenge in the investigation of these newly discovered phases. In this work, we utilize a trapped-ion quantum simulator to observe the signatures of a nonequilibrium driven phase without disorder-the prethermal discrete time crystal. Here, the heating problem is circumvented not by disorder-induced many-body localization, but rather by high-frequency driving, which leads to an expansive time window where nonequilibrium phases can emerge. Floquet prethermalization is thus presented as a general strategy for creating, stabilizing, and studying intrinsically out-of-equilibrium phases of matter.
Prethermal discrete time crystals (DTCs) are a novel phase of periodically driven matter that exhibits robust subharmonic oscillations without requiring disorder. However, previous realizations of prethermal DTCs have relied on the presence of polarization, either spontaneous or induced. Here we introduce a class of prethermal DTCs termed ``unpolarized prethermal discrete time crystals'' (UPDTCs) that arise without any uniform or staggered polarization and propose an experiment to observe them in current trapped-ion quantum simulators. By studying a model of trapped ions using a quantum circuit simulator, we demonstrate that robust period-doubled dynamics can persist in the autocorrelation function of the staggered magnetization, even though its expectation value does not exhibit such dynamics. The period-doubled dynamics is not explained by the classical picture of flipping spins but by quantum fluctuations. We establish that UPDTCs are exponentially long-lived in the high-frequency driving regime, a hallmark of prethermalization. These results expand the known phenomenology and mechanism of prethermal time crystals and underscore the role of quantum effects in stabilizing novel nonequilibrium phases.
We prove the existence of non-equilibrium phases of matter in the prethermal regime of periodically-driven, long-range interacting systems, with power-law exponent α>d\alpha > dα>d, where ddd is the dimensionality of the system. In this context, we predict the existence of a disorder-free, prethermal discrete time crystal in one dimension -- a phase strictly forbidden in the absence of long-range interactions. Finally, using a combination of analytic and numerical methods, we highlight key experimentally observable differences between such a prethermal time crystal and its many-body localized counterpart.
A time crystal is a state of periodically driven matter that breaks discrete time-translation symmetry.Time crystals have been demonstrated experimentally in various programmable quantum simulators, and they exemplify how nonequilibrium, driven quantum systems can exhibit intriguing and robust properties absent in systems at equilibrium.These robust driven states need to be stabilized by some mechanism, with the preeminent candidates being many-body localization and prethermalization.This introduces additional constraints that make it challenging to experimentally observe time crystallinity in naturally occurring systems.Recent theoretical work has developed the notion of prethermalization without temperature, expanding the class of time-crystal systems to explain time-crystalline observations at (or near) infinite temperature.In this work, we conclusively observe the emergence of a prethermal Uð1Þ time-crystalline state at quasi-infinite temperature in a solid-state NMR quantum emulator by verifying the requisites of prethermalization without temperature.In addition to observing the signature period-doubling behavior, we show the existence of a long-lived prethermal regime whose lifetime is significantly enhanced by strengthening an emergent Uð1Þ conservation law.Not only do we measure this enhancement through the global magnetization, but we also exploit on-site disorder to measure local observables, ruling out the possibility of many-body localization and confirming the emergence of long-range correlations.
Time crystals are nonequilibrium phases of matter characterized by the emergence of temporal ordering, in which an interacting many-body system develops robust structure in its time evolution that is not trivially dictated by the external driving or environment. While related phenomena have long been studied in classical nonlinear systems, their realization in entangled quantum matter represents a distinct frontier. The theoretical understanding of discrete time crystals has substantially advanced, yet recent experiments using modern quantum devices and quantum processors reveal regimes beyond established paradigms. These developments call for an extended classification of time-crystalline phases according to both their stabilization mechanisms and their physical character, including discrete and continuous, closed and open, critical, topological, quasiperiodic, and controlled realizations. We review recent implementations of time crystals on quantum platforms and propose such a classification framework, identifying promising directions for the discovery of novel time-crystalline phases of matter.