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arXiv:2605.25667

Dissipative Time Quasicrystals from Multilevel Interference

Kang Shen, Xiangming Hu, Fei Wang

quant-phSubmitted May 25, 2026• Announced May 26, 2026• 0 citations
v1 · May 25, 2026v2 · May 26, 2026
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Abstract

Boundary time crystals exhibit spontaneous breaking of continuous time-translation symmetry through persistent periodic oscillations in driven-dissipative many-body systems. Here, we show that multilevel interference provides a natural route beyond periodic order, enabling dissipative time quasicrystals without externally imposed quasiperiodic driving. We consider a collectively driven-dissipative four-level ensemble with two degenerate excited states and two degenerate ground states. In the thermodynamic limit, the exact mean-field dynamics reduces to an irrational flow on a two-dimensional torus, yielding quasiperiodic order parameters with discrete spectra generated by two incommensurate fundamental frequencies. Vanishing maximal Lyapunov exponents demonstrate that the nonlinear self-consistent dynamics remains nonchaotic. Our results establish a minimal interference-induced mechanism for time-quasiperiodic order and open a route toward higher-dimensional quasiperiodic dynamics in multilevel systems.

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6+13 pages, 2 figures

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Boundary time crystals exhibit spontaneous breaking of continuous time-translation symmetry through persistent periodic oscillations in driven-dissipative many-body systems. Here, we show that multilevel interference provides a natural route beyond periodic order, enabling dissipative time quasicrystals without externally imposed quasiperiodic driving. We consider a collectively driven-dissipative four-level ensemble with two degenerate excited states and two degenerate ground states. In the thermodynamic limit, the exact mean-field dynamics reduces to an irrational flow on a two-dimensional torus, yielding quasiperiodic order parameters with discrete spectra generated by two incommensurate fundamental frequencies. Vanishing maximal Lyapunov exponents demonstrate that the nonlinear self-consistent dynamics remains nonchaotic. Our results establish a minimal interference-induced mechanism for time-quasiperiodic order and open a route toward higher-dimensional quasiperiodic dynamics in multilevel systems.
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Boundary time crystals are a class of exotic dissipative quantum phases that spontaneously break continuous time-translation symmetry in the thermodynamic limit of open quantum systems. In finite-size systems, the long-time evolution of boundary time crystals exhibits decaying oscillations that cannot be captured by widely used mean-field theory. To address this issue, we develop an effective approach called the stroboscopic rotating wave approximation, which provides a well-approximated state for the long-time evolution of boundary time crystals in the strongly driven regime. In this approach, the order parameter exhibits both a long-time decaying envelope governed by an effective Lindblad superoperator and short-time oscillations dominated by a reduced quantum dynamical semigroup. Our results reveal that the competition among dephasing processes along three directions induces persistent oscillations, marking the emergence of the boundary-time-crystal phase. We obtain the analytical expressions for the steady-state density operator, the oscillation period, and the decay rate of the order parameter when the coherent energy splitting exceeds the dissipation rate. Our work provides a beyond-mean-field tool for studying the dynamics of periodically driven open quantum systems and understanding the formation of time crystals.
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
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.
Quasi-periodic driving protocols provide a powerful route to realize novel non-equilibrium phases of matter beyond the Floquet paradigm. However, these protocols inevitably lead to infinite-temperature heat death in isolated systems, which poses a major challenge to their experimental realization. We demonstrate that dissipation can be harnessed to stabilize quasi-periodically driven systems, enabling the realization of robust non-equilibrium phases. Using the paradigmatic open Dicke model, we provide a blueprint for realizing a stable time quasicrystal (TQC) by Fibonacci driving. This TQC is characterized by a robust sub-harmonic quasi-periodic response that is dictated by, but qualitatively distinct from the external Fibonacci drive. By directly analyzing the time evolution in the thermodynamic limit, we establish the existence of TQC order in this system for a wide parameter regime. We trace the origin of the stability of the TQC to the attractor structure induced by dissipation. Strikingly, the TQC order persists in the deep quantum regime with as few as two qubits. We systematically study the dependence of the TQC lifetime, τ∗τ^{\ast}τ∗, on the number of qubits and demonstrate that τ∗τ^{\ast}τ∗ increases monotonically with the system size. Crucially, the TQC is not observed in the absence of dissipation. Our work establishes dissipation as a mechanism for stabilizing non-equilibrium phases of matter under quasi-periodic drive.
Time crystals are many-body states that spontaneously break translation symmetry in time the way that ordinary crystals do in space. While experimental observations have confirmed the existence of discrete or continuous time crystals, these realizations have relied on the utilization of periodic forces or effective modulation through cavity feedback. The original proposal for time crystals is that they would represent self-sustained motions without any external periodicity, but realizing such purely self-generated behavior has not yet been achieved. Here, we provide theoretical and experimental evidence that many-body interactions can give rise to an inherent time crystalline phase. Following a calculation that shows an ensemble of pumped four-level atoms can spontaneously break continuous time translation symmetry, we observe periodic motions in an erbium-doped solid. The inherent time crystal produced by our experiment is self-protected by many-body interactions and has a measured coherence time beyond that of individual erbium ions.