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arXiv:2602.05994

Dissipation stabilizes Dicke Time Quasicrystals

Sk Anisur, Shuva Mondal, Tanaya Ray, Sayan Choudhury

quant-phcond-mat.quant-gascond-mat.stat-mechSubmitted Feb 5, 2026• Announced Feb 6, 2026• 0 citations• Revised Aug 11, 2026 (v2)
v1 · Feb 5, 2026v2 · Aug 11, 2026
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Abstract

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, $τ^{\ast}$, on the number of qubits and demonstrate that $τ^{\ast}$ 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.

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7+2 pages, 4 figures

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The classification of phases of matter has been revolutionised by topological order and non equilibrium phenomena such as time crystals. However, a unified framework connecting temporal order, topology, and dissipation remains elusive. Here we introduce the concept of "Time-Quasicrystals"—non-equilibrium topological phases that exhibit quasi-periodic temporal order protected by dissipative dynamics. These phases emerge in driven dissipative quantum systems through the interplay of Floquet engineering and non-local dissipation, leading to an effective non-Hermitian Floquet Hamiltonian with topological edge modes in the frequency domain. We demonstrate three hallmarks of Time-Quasicrystals: (1) fractal-like temporal correlations with multiple incommensurate frequencies, (2) a quantised topological invariant robust against disorder, and (3) algebraically decaying memory of phase perturbations. We provide explicit experimental realisations in Rydberg atom arrays and circuit quantum electrodynamics platforms. Our work establishes Time-Quasicrystals as a bridge between topological phases, time crystals, and quantum simulation, opening pathways to dissipative protected quantum memory and novel non-equilibrium quantum phenomena.
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A discrete time crystal (DTC) is a remarkable non-equilibrium phase of matter characterized by the persistent sub-harmonic oscillations of physical observables in periodically driven many-body systems. Motivated by the question of whether such a temporal periodic order can persist when the drive becomes aperiodic, we investigate the dynamics of a Lipkin-Meshkov-Glick model under quasi-periodic Thue-Morse (TM) driving. Intriguingly, this infinite-range-interacting spin system can host "quasi-discrete time crystal" (quasi-DTC) phases characterized by periodic oscillations of the magnetization. We demonstrate that our model can host the quasi-DTC analog of both period-doubling DTCs as well as higher-order DTCs. These quasi-DTCs are robust to various perturbations, and they originate from the interplay of "all-to-all" interactions and the recursive structure of the TM sequence. Our results suggest that quasi-periodic driving protocols can provide a promising route for realizing novel non-equilibrium phases of matter in long-range interacting systems.