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arXiv:2404.06890 · Physical Review A

Discrete time crystals in the presence of non-Markovian dynamics

Bandita Das, Noufal Jaseem, Victor Mukherjee

Published Jul 10, 2024• 1 citation
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Abstract

We study discrete time crystals (DTCs) in periodically driven quantum systems, in the presence of non-Markovian dissipation. In contrast to DTCs observed in earlier works in the presence of Markovian dynamics, using the open Dicke model in presence of Jaynes-Cummings-like dissipation, we show that non-Markovian regime can be highly beneficial for stabilizing DTCs over a wide range of parameter values. This may be attributed to periodically varying dissipation rates even at long times in the case of non-Markovian dynamics. Further the Markovian and non-Markovian regimes show sharp distinctions for intermediate strengths of the dissipator coefficient, with a time-independent steady state in the Markovian regime being replaced by varied dynamical phases, including DTC order, in the non-Markovian regime. We also verify the robustness of the DTC phase in the non-Markovian regime by introducing errors both in the Hamiltonian as well as in the dissipation. Our study shows the possibility of using DTC as a probe for non-Markovian dynamics in periodically modulated open quantum systems, at long times.

DOI
10.1103/physreva.110.012208

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We study discrete time crystals (DTCs) in periodically driven quantum systems, in the presence of non-Markovian dissipation. In contrast to DTCs observed in earlier works in the presence of Markovian dynamics, using the open Dicke model in presence of Jaynes-Cummings-like dissipation, we show that non-Markovian regime can be highly beneficial for stabilizing DTCs over a wide range of parameter values. This may be attributed to periodically varying dissipation rates even at long times in the case of non-Markovian dynamics. Further the Markovian and non-Markovian regimes show sharp distinctions for intermediate strengths of the dissipator coefficient, with a time-independent steady state in the Markovian regime being replaced by varied dynamical phases, including DTC order, in the non-Markovian regime. We also verify the robustness of the DTC phase in the non-Markovian regime by introducing errors both in the Hamiltonian as well as in the dissipation. Our study shows the possibility of using DTC as a probe for non-Markovian dynamics in periodically modulated open quantum systems, at long times.
We study Boundary time crystals (BTCs) in the presence of non-Markovian dynamics. In contrast to BTCs observed in earlier works in the Markovian regime, we show that non-Markovian dynamics can be highly beneficial for stabilizing BTCs over a wide range of parameter values, even in the presence of intermediate rates of dissipation. Notably, we also observe the emergence of higher-order limit cycles (HO-LCs) for some parameter regimes. We analyze the effect of non-Markovian dynamics on BTCs and HO-LCs using quantum Fisher information, time-averaged magnetization, a measure of non-Markovianity, and a dynamical phase diagram, all of which show complex behaviors with changing non-Markovianity parameters. Our studies can pave the way for stabilizing time crystals in dissipative systems, as well as lead to studies on varied dissipative dynamics on time translational symmetry breaking.
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.
Discrete time crystals (DTCs) exhibit a special nonequilibrium phase of matter in periodically driven many-body systems with spontaneous breaking of time translational symmetry. The presence of decoherence generally enhances thermalization and destroys the coherence required for the existence of DTCs. In this paper, we devise a mechanism for establishing a stable DTC with period-doubling oscillations in an open quantum system that is governed by a properly tailored non-Hermitian Hamiltonian. We find a specific class of nonreciprocal couplings in our non-Hermitian dynamics which prevents thermalization through eigenstate ordering. This choice of non-Hermitian dynamics significantly enhances the stability of the DTC against imperfect pulses. Through a comprehensive analysis, we determine the phase diagram of the system in terms of pulse imperfection.
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.
Discrete time crystals (DTCs) are phases of matter characterized by the presence of an observable evolving with nTnTnT periodicity under a TTT-periodic Hamiltonian, where n>1n>1n>1 is an integer insensitive to small parameter variations. In particular, DTCs with n=2n=2n=2 have been extensively studied in periodically quenched and kicked spin systems in recent years. In this paper, we study the emergence of DTCs in a many-body system whose semiclassical mean-field dynamics is nonintegrable, using a rather simple model depicting a harmonically driven spin chain. We advocate to first employ a semiclassical approximation to arrive at a mean-field Hamiltonian and then identify the parameter regime at which DTCs exist, with standard tools borrowed from studies of classical chaos. Specifically, we seek symmetric-breaking solutions by examining the stable islands on the Poincar\'e surface of section of the mean-field Hamiltonian. We then turn to the actual many-body quantum system, evaluate the stroboscopic dynamics of the total magnetization in the full quantum limit, and verify the existence of DTCs. Our effective and straightforward approach indicates that in general DTCs are one natural aspect of many-body quantum chaos with mixed classical phase space structure. Our approach can also be applied to general time-periodic systems, which is thus promising for finding DTCs with n>2n>2n>2 and opening possibilities for exploring DTCs properties beyond their time-translational breaking features.
We investigate the dynamics of coupled discrete time crystals (DTCs) in the coupled Dicke model or Dicke dimer (DD) with dissipation. By numerically simulating the mean-field dynamics of the system, we show that coupling two DTCs decreases their oscillation amplitude following a transient relaxation period. For sufficiently strong coupling, the coupled DTCs become unstable, resulting in the system relaxing towards the normal phase (NP). We demonstrate that the relaxation time diverges near the critical coupling strength, suggesting a continuous phase transition. Using the truncated Wigner approximation (TWA), we explore how the dynamics are affected by the introduction of quantum fluctuations. We also consider a scenario in which an NP is briefly coupled to a DTC, seeding the NP to transform into a DTC that is either synchronized or anti-synchronized relative to the DTC. We investigate the robustness of this phenomenon in the presence of noise. Using these results, we propose a scheme to perform NAND and NOR operations with three DTCs by sequentially coupling the input and output sites. We identify the parameter regimes in which the logic gate architecture remains valid, and investigate how the protocol is affected by the presence of quantum fluctuations.