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时间晶体是一种特殊的物质状态，它指多体系统在内部自组织的作用下，自发产生时间周期性振荡的现象。近期，无需外部周期性驱动的连续时间晶体已在耗散固体材料中实现，并呈现出长时间稳定振荡的特性。然而，在多体系统中，连续时间晶体的系统参数，包括原子间相互作用强度、均匀性、频率失谐以及驱动场强度等，均呈现高度的复杂性和关联性；这些参数对连续时间晶体振荡周期形成的物理机制和耦合效应的影响尚不明确。本文基于掺铒晶体中构建的连续时间晶体，通过理论分析揭示了时间晶体振荡周期与驱动光场强度、偶极-偶极相互作用、原子间跃迁强度差异以及耗散系数之间的内在关联。研究表明，即便在这些参数动态变化引起的扰动下，时间晶体的振荡周期仍展现出显著的鲁棒性。Continuous time crystals represent a novel state of many-body systems, self-organizing into timeperiodic oscillations without the need for external periodic driving. Recent experiments have demonstrated the realization of such systems in dissipative solid-state materials, where persistent temporal order is autonomously sustained. A defining characteristic of time crystals is their robustness, signifying the ability to maintain rhythmic behavior despite various disturbances, including fluctuations in internal parameters and external noise., which is of both scientific value and potential for technological applications Although prior studies have established the existence of robustness in specific experimental parameters, a systematic framework for quantifying and predicting their resilience to perturbations is lacking, and the underlying physics of this robustness remains inadequately understood. Key unresolved questions 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 paper addresses these gaps by systematically analyzing how internal parameters and external influences affect the oscillation period and overall stability. Internally, the dynamics are dictated by dipoledipole interactions and atomic transition strengths, which define the system’ s emergent temporal symmetry breaking. Externally, the system’ s response is controlled by the intensity of the optical driving field and the rates of energy dissipation. A key finding is the identification of an intrinsic feedback mechanism that dynamically stabilizes the time crystal. This mechanism acts as a restorative force, correcting for deviations caused by minor disturbances and maintaining the coherence of the oscillatory phase.
Moreover, the system displays nonlinear dynamical behavior, characterized by two distinct regimes: one where stable oscillations continue under moderate disturbances, and another where stronger disturbances induce a dynamical phase transition, leading to disordered states or a switch between dynamically unstable and stable states. These results provide a thorough understanding of the diverse behaviors observed in continuous time crystals and create a vital theoretical foundation for exploiting their unique properties in advanced applications like quantum information processing and precision metrology.-
Keywords:
- continuous-time crystals /
- many-body systems /
- erbium-doped crystals /
- periodic oscillations /
- robustness
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