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arXiv:2311.08899 · Physical Review Research

Self-organized time crystal in driven-dissipative quantum system

Ya-Xin Xiang, Qun‐Li Lei, Zhengyang Bai, Yu‐qiang Ma

Published Aug 19, 2024• 4 citations
arXivHTMLPDF

Abstract

Continuous time crystals (CTCs) are characterized by sustained oscillations that break the time-translation symmetry. Since the ruling out of equilibrium CTCs by no-go theorems, the emergence of such dynamical phases has been observed in various driven-dissipative quantum platforms. The current understanding of CTCs is mainly based on mean-field theories, which fail to address the problem of whether the continuous time-translation symmetry can be broken in noisy, spatially extended systems absent in all-to-all couplings. Here, we propose a CTC realized in a quantum contact model through self-organized bistability. The CTCs stem from the interplay between collective dissipation induced by the first-order absorbing phase transitions and slow constant driving provided by an incoherent pump. The stability of such oscillatory phases in finite dimensions under the action of intrinsic quantum fluctuations is scrutinized by the functional renormalization group method and numerical simulations. Occurring at the edge of many-body synchronization, the CTC phase exhibits an inherent period and amplitude with a coherence time linearly diverging with system size, thus also constituting a boundary time crystal. Our results serve as a solid route towards self-protected CTCs in strongly interacting open systems. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.033185

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Continuous time crystals (CTCs) are characterized by sustained oscillations that break the time-translation symmetry. Since the ruling out of equilibrium CTCs by no-go theorems, the emergence of such dynamical phases has been observed in various driven-dissipative quantum platforms. The current understanding of CTCs is mainly based on mean-field theories, which fail to address the problem of whether the continuous time-translation symmetry can be broken in noisy, spatially extended systems absent in all-to-all couplings. Here, we propose a CTC realized in a quantum contact model through self-organized bistability. The CTCs stem from the interplay between collective dissipation induced by the first-order absorbing phase transitions and slow constant driving provided by an incoherent pump. The stability of such oscillatory phases in finite dimensions under the action of intrinsic quantum fluctuations is scrutinized by the functional renormalization group method and numerical simulations. Occurring at the edge of many-body synchronization, the CTC phase exhibits an inherent period and amplitude with a coherence time linearly diverging with system size, thus also constituting a boundary time crystal. Our results serve as a solid route towards self-protected CTCs in strongly interacting open systems. Published by the American Physical Society 2024
Time crystals are a nonequilibrium phase of matter that extend fundamental spontaneous symmetry breaking into the temporal dimension, typically requiring external driving for their realization. Here, we explore the nonequilibrium phase diagram of a two-dimensional dissipative Heisenberg spin system without external coherent or incoherent driving. Through numerical analysis of spin dynamics, we identify nonstationary steady states, some of which are limit cycles with persistent periodic oscillations, while others exhibit chaotic, aperiodic behavior. The emergence of limit cycle steady states breaks the continuous time-translation symmetry of this time-independent many-body system, classifying them as continuous time crystals. We further validate these oscillatory behaviors by testing their stability against local perturbations and assess the robustness of the emergent continuous time crystals by introducing isotropic Gaussian white noise. This work provides insights into the intricate interplay between the dissipation and spin interaction, and opens possibilities for realizing dissipation-induced, heating-immune time crystals. Time crystals represent a nonequilibrium phase of matter without an equilibrium counterpart. The authors investigate the nonequilibrium steadystate phase diagram of a two-dimensional dissipative Heisenberg model in the absence of driving, and identify a continuous time crystalline phase exhibiting persistent oscillations in time.
Continuous time crystals represent a novel state in many-body systems that can self-organize into timeperiodic oscillations without external periodic driving. Recent experiments have achieved such systems in dissipative solid-state materials, where persistent temporal order is autonomously sustained. A decisive characteristic of time crystals is their robustness, meaning that despite various disturbances, including fluctuations in internal parameters and external noise, they can still maintain rhythmic behavior, which has scientific value and echnological application potential. Although previous studies have shown that specific experimental parameters have robustness, thare is a lack of a systematic framework for quantifying and predicting their resilience to disturbances, and the underlying physics of this robustnessis still not fully understood. The key unresolved problems include how nonlinear interactions and feedback mechanisms contribute to stability, and what the critical thresholds are for parameter variations beyond which temporal order collapses. This work addresses these gaps by systematically analyzing how internal parameters and external influences affect the oscillation period and overall stability. Internally, the dynamics are determined by dipole-dipole interactions and atomic transition strengths, which define the temporal symmetry breaking that occurs in the system. Externally, the response of the system is controlled by the strength of the optical driving field and the energy dissipation rate. A key finding is the determination of an intrinsic feedback mechanism for a dynamically stabile time crystal. This mechanism plays a role in restoring force, correcting deviations caused by minor disturbances, and maintaining the coherence of oscillatory phase. Moreover, the system displays nonlinear dynamical behavior, characterized by two different states: one is stable oscillation continuing under moderate disturbance, and the other is stronger disturbance causing dynamical phase transition, resulting in switching between disordered or dynamically unstable state and stable state. These results provide a comprehensive understanding of the various behaviors observed in continuous time crystals and lay an important theoretical foundation for utilizing their unique properties in advanced applications such as quantum information processing and precision metrology.
Continuous time crystals, i.e., nonequilibrium phases with a spontaneously broken continuous time-translational symmetry, have been studied and recently observed in the long time dynamics of open quantum systems. Here, we investigate a lattice of interacting three-level particles and find two distinct time-crystal phases that cannot be described within mean-field theory. Remarkably, one of them emerges only in the presence of correlations, upon accounting for beyond-mean-field effects. Our findings extend explorations of continuous time-translational symmetry breaking in dissipative systems beyond the classical phenomenology of periodic orbits in a low-dimensional nonlinear system. The proposed model applies directly to the laser-driven dynamics of interacting Rydberg states in neutral-atom arrays and suggests that the predicted time-crystal phases are observable in such experiments.
The breaking of the continuous time-translation symmetry manifests, in Markovian open quantum systems, through the emergence of nonstationary dynamical phases. Systems that display nonequilibrium transitions into these phases are referred to as time crystals, and they can be realized, for example, in many-body systems governed by collective dissipation and long-ranged interactions. Here, we provide a complete analytical characterization of a boundary time-crystal phase transition. This involves exact expressions for the order parameter and for the dynamics of quantum fluctuations, which, in the time-crystalline phase, remains asymptotically non-Markovian as a consequence of the time-translation symmetry breaking. We demonstrate that boundary time crystals are intrinsically critical phases, where fluctuations exhibit a power-law divergence with time. Our results show that a dissipative time-crystal phase is far more than merely a classical nonlinear and nonstationary (limit cycle) dynamics of a macroscopic order parameter. It is rather a genuine many-body phase where the properties of correlations distinctly differ from those of stationary ones.
Driven-dissipative many-body systems support nontrivial quantum phases absent in equilibrium. As a prominent example, the interplay between coherent driving and collective dissipation can lead to a dynamical quantum phase that spontaneously breaks time-translation symmetry. This so-called boundary time crystal (BTC) is fragile in the presence of local dissipation, which can easily relax the system to a stationary state. In this Letter, we demonstrate a robust BTC that is intrinsically induced by local dissipation. We provide extensive numerical evidence to support the existence of the BTC and study its behaviors in different regimes. In particular, with decreasing interaction range, we identify a transition from mean-field limit cycles to correlated BTCs featuring sizable quantum correlations. Our studies significantly broaden the scope of nonequilibrium phases and shed new light on the experimental search for dynamical quantum matter.
Continuous time crystals (CTCs) represent a nonequilibrium quantum phase that spontaneously breaks time-translation symmetry without periodic external driving, manifesting as persistent, long-lived oscillations under steady pumping. The lifetime is constrained by the instability of the limit cycle phase, balanced between nonlinear feedback and energy dissipation, which have rarely been studied in experiments before. Here, we report an observation of an ultralong-lived Rydberg-atom CTC in a driven-dissipative many-body atomic system. By harnessing long-range interactions and engineering a dissipative environment that stabilizes the limit-cycle dynamics, we suppress heating and decay effects that typically destroy time-crystalline order. The key factor underlying the ultralong-lived CTC is the closing of the Liouvillian gap and the near-zero real part of the system's Liouvillian eigenspectrum. Through systematic optimization, we achieve an oscillatory lifetime exceeding 16.95 hours-orders of magnitude longer than previous CTC realizations. Our work establishes a robust platform for exploring long-lived autonomous nonequilibrium phases and paves the way for applications in quantum sensing and continuous-time quantum information processing.