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arXiv:2102.01695 · Science

Observation of a prethermal discrete time crystal

A. Kyprianidis, Francisco Machado, William Morong, Patrick Becker, K. S. Collins, Dominic V. Else, Lei Feng, Paul Hess, Chetan Nayak, Guido Pagano, Norman Y. Yao, Christopher R. Monroe

Published Jun 10, 2021• 219 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1126/science.abg8102

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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.
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
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.
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.
We demonstrate that the prethermal regime of periodically driven (Floquet), classical many-body systems can host nonequilibrium phases of matter. In particular, we show that there exists an effective Hamiltonian that captures the dynamics of ensembles of classical trajectories despite the breakdown of this description at the single trajectory level. In addition, we prove that the effective Hamiltonian can host emergent symmetries protected by the discrete time-translation symmetry of the drive. The spontaneous breaking of such an emergent symmetry leads to a subharmonic response, characteristic of time crystalline order, that survives to exponentially late times in the frequency of the drive. To this end, we numerically demonstrate the existence of classical prethermal time crystals in systems with different dimensionalities and ranges of interaction. Extensions to higher order and fractional time crystals are also discussed.
Floquet (periodically driven) systems can give rise to unique nonequilibrium phases of matter without equilibrium analogs. The most prominent example is the realization of discrete time crystals. An intriguing question emerges: What other novel phases can manifest when the constraint of time periodicity is relaxed? In this study, we explore quantum systems subjected to a quasiperiodic drive. Leveraging a strongly interacting spin ensemble in diamond, we identify the emergence of long-lived discrete time quasicrystals. Unlike conventional time crystals, time quasicrystals exhibit robust subharmonic responses at multiple incommensurate frequencies. Furthermore, we show that the multifrequency nature of the quasiperiodic drive allows for the formation of diverse patterns associated with different discrete time quasicrystalline phases. Our findings demonstrate the existence of nonequilibrium phases in quasi-Floquet settings, significantly broadening the catalog of novel phenomena in driven many-body quantum systems.
Motivated by experimental observations of time-symmetry breaking behavior in a periodically driven (Floquet) system, we study a one-dimensional spin model to explore the stability of such Floquet discrete time crystals (DTCs) under the interplay between interaction and the microwave driving. For intermediate interactions and high drivings, from the time evolution of both stroboscopic spin polarization and mutual information between two ends, we show that Floquet DTCs can exist in a prethermal time regime without the tuning of strong disorder. For much weak interactions the system is a symmetry-unbroken phase, while for strong interactions it gives its way to a thermal phase. Through analyzing the entanglement dynamics, we show that large driving fields protect the prethermal DTCs from many-body localization and thermalization. Our results suggest that by increasing the spin interaction, one can drive the experimental system into optimal regime for observing a robust prethermal DTC phase.