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New Journal of Physics

Signatures of discrete time crystalline order in dissipative spin ensembles

James O’Sullivan, Oliver Lunt, Christoph W. Zollitsch, Mike L. W. Thewalt, John J. L. Morton, Arijeet Pal

Published Aug 1, 2020• 37 citations
Publisher

Abstract

Abstract Discrete time-translational symmetry in a periodically driven many-body system can be spontaneously broken to form a discrete time crystal, an exotic new phase of matter. We present observations characteristic of discrete time crystalline order in a driven system of paramagnetic P-donor impurities in isotopically enriched 28Si cooled below 10 K. The observations exhibit a stable subharmonic peak at half the drive frequency which remains pinned even in the presence of pulse error, a signature of discrete time crystalline order. This signal has a finite lifetime of ∼100 Floquet periods, but this effect is long-lived relative to coherent spin–spin interaction timescales, lasting ∼104 times longer. We present simulations of the system based on the paradigmatic central spin model and show good agreement with experiment. We investigate the role of dissipation and interactions within this model, and show that both are capable of giving rise to discrete time crystal-like behaviour.

DOI
10.1088/1367-2630/ab9fbe

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Abstract Discrete time-translational symmetry in a periodically driven many-body system can be spontaneously broken to form a discrete time crystal, an exotic new phase of matter. We present observations characteristic of discrete time crystalline order in a driven system of paramagnetic P-donor impurities in isotopically enriched 28Si cooled below 10 K. The observations exhibit a stable subharmonic peak at half the drive frequency which remains pinned even in the presence of pulse error, a signature of discrete time crystalline order. This signal has a finite lifetime of ∼100 Floquet periods, but this effect is long-lived relative to coherent spin–spin interaction timescales, lasting ∼104 times longer. We present simulations of the system based on the paradigmatic central spin model and show good agreement with experiment. We investigate the role of dissipation and interactions within this model, and show that both are capable of giving rise to discrete time crystal-like behaviour.
Periodically driven quantum systems host a range of non-equilibrium phenomena which are unrealizable at equilibrium. Discrete time-translational symmetry in a periodically driven many-body system can be spontaneously broken to form a discrete time crystal, a putative quantum phase of matter. We present the observation of discrete time crystalline order in a driven system of paramagnetic PPP -donor impurities in isotopically enriched 28Si^{28}Si28Si cooled below 101010 K. The observations exhibit a stable subharmonic peak at half the drive frequency which remains pinned even in the presence of pulse error, a signature of DTC order. We propose a theoretical model based on the paradigmatic central spin model which is in good agreement with experimental observations, and investigate the role of dissipation in the stabilisation of the DTC. Both experiment and theory indicate that the order in this system is primarily a dissipative effect, and which persists in the presence of spin-spin interactions. We present a theoretical phase diagram as a function of interactions and dissipation for the central spin model which is consistent with the experiments. This opens up questions about the interplay of coherent interaction and dissipation for time-translation symmetry breaking in many-body Floquet systems.
A discrete time crystal is an out-of-equilibrium phase of matter characterized by the spontaneous breaking of discrete time-translation symmetry. Using extensive numerical simulations based on matrix-product-state methods, we provide evidence for discrete time-crystalline behavior in strongly disordered spin chains with Heisenberg interactions, including the isotropic point, subject to periodic driving. Starting from a many-body localized regime, we observe that rotations induced by delta kicks produce a pronounced subharmonic response at half the drive frequency in spin observables. We investigate the stability of this response against rotation-angle errors through entanglement entropy, quantum Fisher information, short-range spin correlations, and restricted-control ergotropy. Increasing the rotation error reveals an intermediate dynamical regime separating the time-crystalline and Floquet-localized responses. In this regime, most observables exhibit signatures of weakly correlated dynamics reminiscent of Anderson localization.
Nonequilibrium driving systems provide fertile ground for exploring intriguing spontaneous symmetry breaking phenomena. In this paper, we report on the intertwined discrete spacetime translational symmetry breaking in a driven-dissipative spin system without pure spatial translational symmetry, resulting in the emergence of an out-of-equilibrium nonmagnetic phase termed the ``discrete spacetime crystal.'' In contrast to the previously widely studied discrete time crystal, the spins establish a distinctive long-range crystalline order not only in time, but also in the intertwined spacetime direction. We further demonstrate the exponentially long lifetime of the spatial-temporal order against generic weak environmental noise fluctuations. Finally, possible experimental realizations of our model are discussed. Our findings shed light on the existence of exotic phases of matter characterized by intertwined spacetime symmetry breaking, paving the way for future investigations into the properties and potential applications of these exotic states.
We analyze the quantum dynamics of periodically driven, disordered systems in the presence of long-range interactions. Focusing on the stability of discrete time crystalline (DTC) order in such systems, we use a perturbative procedure to evaluate its lifetime. For 3D systems with dipolar interactions, we show that the corresponding decay is parametrically slow, implying that robust, long-lived DTC order can be obtained. We further predict a sharp crossover from the stable DTC regime into a regime where DTC order is lost, reminiscent of a phase transition. These results are in good agreement with the recent experiments utilizing a dense, dipolar spin ensemble in diamond [Nature (London) 543, 221 (2017)NATUAS0028-083610.1038/nature21426]. They demonstrate the existence of a novel, critical DTC regime that is stabilized not by many-body localization but rather by slow, critical dynamics. Our analysis shows that the DTC response can be used as a sensitive probe of nonequilibrium quantum matter.
Abstract Periodically driven quantum systems manifest various non-equilibrium features which are absent at equilibrium. For example, discrete time-translation symmetry can be broken in periodically driven quantum systems leading to an exotic phase of matter, called discrete time crystal (DTC). For open quantum systems, previous studies showed that DTC can be found only when there exists a meta-stable state in the undriven system. However, by investigating the simplest Bose–Hubbard model with dissipation and time periodically tunneling, we find in this paper that a 2T DTC can appear even when the meta-stable state is absent in the undriven system. This observation extends the understanding of DTC and shed more light on the physics behind the DTC. Besides, by the detailed analysis of simplest two-sites model, we show further that the two-sites model can be used as basic building blocks to construct large rings in which a nT DTC might appear. These results might find applications into engineering exotic phases in driven open quantum systems.
Abstract Discrete time-crystals are periodically driven quantum many-body systems with broken discrete time translational symmetry, a non-equilibrium steady state representing self-organization of motion of quantum particles. Observations of discrete time-crystalline order are currently limited to magneto-optical experiments and it was never observed in a transport experiment performed on systems connected to external electrodes. Here we demonstrate that both discrete time-crystal and quasi-crystal survive a very general class of environments corresponding to single-particle gain and loss through system-electrode coupling over experimentally relevant timescales. Using dynamical symmetries, we analytically identify the conditions for observing time-crystalline behavior in a periodically driven open Fermi-Hubbard chain attached to electrodes. We show that the spin-polarized transport current directly manifests the existence of a time-crystalline behavior. Our findings are verifiable in present-day experiments with quantum-dot arrays and Fermionic ultra-cold atoms in optical lattices.