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arXiv:2004.04005 · New Journal of Physics

Discrete time-crystalline order in Bose–Hubbard model with dissipation

C M Dai, Z C Gu, X X Yi

Published Jan 22, 2020• 5 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1367-2630/ab6ead

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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.
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 (DTC) is an essentially nonequilibrium phase that breaks discrete time-translation symmetry in periodically driven (Floquet) systems.In ideal isolated quantum systems without dissipation, many kinds of DTCs have been theoretically proposed and experimentally verified in various artificial quantum systems, such as trapped ions, NV centers in diamond, and quantum computers.However, in real physical systems, we cannot avoid dissipation stemming from coupling to an external environment.Nevertheless, the effects of dissipation on DTCs have not been fully explored yet.This thesis reports the author's two original studies on dissipative DTCs.First, we formulate a symmetry-based theory of dissipative DTCs.To this end, we introduce Floquet dynamical symmetry (FDS) governing the long-time dynamics of dissipative Floquet systems.The FDS protects the quantum coherence of the system from dissipation and dephasing and leads to two types of time crystals: the discrete time crystal (DTC) and discrete time quasicrystal (DTQC), which are different in periodicity.We show that these time crystals appear in spin-S Bose-and Fermi-Hubbard models driven by an ac field and that their periodicity can be tuned by adjusting the field strength.Since these time crystals rely on the FDS alone, they appear even in the presence of perturbations as long as the FDS exists.We also elucidate that the FDS explains the symmetry structure behind the conventional DTCs proposed in the previous studies.Second, we investigate dissipative DTCs in solid-state materials by considering a dissipative quantum Ising model periodically driven by π-pulses.While the previous studies on dissipative DTCs have focused on well-controllable artificial quantum systems, we show that realistic dissipation in solids does not destroy but can stabilize the DTC order.Using the time-dependent mean-field theory, we analyze the DTC phase transition and determine critical exponents, including a dynamical one.We also find a novel reentrant phase transition in varying the pulse interval.This transition is due to a nontrivial interplay of the periodic drive and dissipation and has no equilibrium counterparts in the corresponding undriven system.Furthermore, to demonstrate the rigidity (stability) of the DTC, we consider imperfect πpulses, showing that the DTC is robust against minor imperfections and finding that DTQC appears for major imperfections.These results uncover a general symmetry aspect of dissipative DTCs and lay the foundation for realizing DTCs in material science.
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.
Discrete-Time Crystals (DTC) are a non-equilibrium phase of matter characterized by the breaking of time-translation symmetry in periodically driven quantum systems. In this work, we present a detailed thermodynamic analysis of a DTC in a one-dimensional spin-1/2 chain coupled to a thermal bath. We derive a master equation from the microscopic model, and we explore key thermodynamic quantities, such as work, heat, and entropy production. Our results reveal that the DTC signature inevitably decays in the presence of environmental noise, but we show that a periodic measurement scheme can mitigate the effects of decoherence, stabilizing the subharmonic oscillations of the DTC for extended periods. These findings provide insights into the robustness of time-crystalline phases and potential strategies for protecting them in experimental settings.
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.
The engineering of new states of matter through Floquet driving has revolutionized the field of condensed matter physics. This technique enables the creation of hybrid topological states and ordered phases that are absent in normal systems. Crystalline structures, exemplifying spatially ordered systems under periodic driving, have been extensively studied. However, recent focus has shifted towards discrete time crystals (DTCs), periodically driven quantum many-body systems that break time translation symmetry under specific conditions. In this paper, the model of discrete time crystals is extended to allow for the formation of time-varying tesseracts, allowing for the investigation of time translational symmetry in pseudo-higher-dimensional lattice systems.