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Communications Physics

Discrete time quasi-crystals in Rydberg atomic chain

Xiaofan Luo, Yaoting Zhou, Z. S. Xu, Weilun Jiang

Published Mar 9, 2026• 0 citations
Publisher

Abstract

Abstract Discrete time quasi-crystals are non-equilibrium phenomena with quasi-periodic order in time domain, an extension of the discrete time-crystal phase. As a natural platform to explore the non-equilibrium phases, Rydberg atomic arrays have demonstrated the quantum simulation of the discrete-time crystal phase, associated with quantum many-body scar state. However, the existence of discrete time quasi-crystal in this platform has yet to be conceived. Here, we propose a method to generate the discrete time quasi-crystal behavior by coupling two discrete time-crystals, where two external driving frequencies have the maximum incommensurability. Upon the characterization of the phase diagram and the robustness, we explore the entanglement entropy between two subsystems. We find that the emergence of the aperiodic response appears at an appropriate driving frequency, which could be well interpreted by the model with two coupled oscillators. Our method thus offers the possibilities to explore the phases of matters in the quantum simulator.

DOI
10.1038/s42005-026-02572-0

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Abstract Discrete time quasi-crystals are non-equilibrium phenomena with quasi-periodic order in time domain, an extension of the discrete time-crystal phase. As a natural platform to explore the non-equilibrium phases, Rydberg atomic arrays have demonstrated the quantum simulation of the discrete-time crystal phase, associated with quantum many-body scar state. However, the existence of discrete time quasi-crystal in this platform has yet to be conceived. Here, we propose a method to generate the discrete time quasi-crystal behavior by coupling two discrete time-crystals, where two external driving frequencies have the maximum incommensurability. Upon the characterization of the phase diagram and the robustness, we explore the entanglement entropy between two subsystems. We find that the emergence of the aperiodic response appears at an appropriate driving frequency, which could be well interpreted by the model with two coupled oscillators. Our method thus offers the possibilities to explore the phases of matters in the quantum simulator.
Discrete time quasi-crystals are non-equilibrium quantum phenomena with quasi-periodic order in the time dimension, and are an extension of the discrete time-crystal phase. As a natural platform to explore the non-equilibrium phase of matter, the Rydberg atomic array has implemented the quantum simulation of the discrete-time crystal phase, associated with quantum many-body scar state. However, the existence of discrete time quasi-crystal on the Rydberg cold atom experiment platform has yet to be conceived. Here, we propose a method to generate the discrete time quasi-crystal behavior by coupling two discrete time-crystals, where associated two external driving frequencies have the maximum incommensurability. While we analysis its robustness and compute the phase diagram of corresponding observables. We significantly calculate the entanglement entropy between two parts of the system. Remarkably, we find the emergence of the aperiodic response is indeed caused by interaction between systems via Rydberg blockade effect. Our method thus offers the possibilities to explore the novel phases in quantum simulator.
Discrete time quasicrystals (DTQC) constitute a class of non-equilibrium matter characterized by temporal order without strict periodicity, in contrast to conventional time crystals. Investigating these phenomena is essential for expanding our fundamental understanding of far-from-equilibrium quantum matter and spontaneous symmetry breaking beyond periodic regimes. Here, we experimentally observe a DTQC in a driven-dissipative ensemble of strongly interacting Rydberg atoms, displaying non-equilibrium dynamical response with a different finite Abelian group symmetry Zm×Zn{{\mathbb{Z}}}_{m}\times {{\mathbb{Z}}}_{n}Zm​×Zn​. By applying a quasiperiodic drive using a dual-frequency drive with incommensurate frequencies, we demonstrate that the system exhibits a robust subharmonic response at multiple incommensurate frequencies, signifying the emergence of a DTQC phase. We map the full phase diagram of the system, which includes the DTQC phase, and demonstrate its rigidity against perturbations in both RF field intensity and laser detuning. Moreover, we observe a cyclic group symmetry effect that constrains the construction of Z2×Z3{{\mathbb{Z}}}_{2}\times {{\mathbb{Z}}}_{3}Z2​×Z3​-symmetric DTQC. This work establishes a versatile platform for studying non-equilibrium phases of matter and provides insights into the dynamics of time-translation symmetry breaking in quantum many-body systems. Time-crystal phases have raised both theoretical and experimental interest across various platforms. Here, the authors report the observation of a discrete time-quasicrystal in a driven-dissipative ensemble of interacting Rydberg atoms, advancing the understanding of symmetry breaking in these systems.
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.
Floquet (periodically driven) systems can give rise to unique nonequilibrium phases of matter without equilibrium analogs. The most prominent example is the realization of discrete time crystals. An intriguing question emerges: What other novel phases can manifest when the constraint of time periodicity is relaxed? In this study, we explore quantum systems subjected to a quasiperiodic drive. Leveraging a strongly interacting spin ensemble in diamond, we identify the emergence of long-lived discrete time quasicrystals. Unlike conventional time crystals, time quasicrystals exhibit robust subharmonic responses at multiple incommensurate frequencies. Furthermore, we show that the multifrequency nature of the quasiperiodic drive allows for the formation of diverse patterns associated with different discrete time quasicrystalline phases. Our findings demonstrate the existence of nonequilibrium phases in quasi-Floquet settings, significantly broadening the catalog of novel phenomena in driven many-body quantum systems.
Abstract We investigate the nonlinear dynamics of two coupled driven–dissipative Rydberg atomic chains, each of which formed a previously reported continuous time crystal phase. By tuning the inter-chain interaction, the two time-crystalline subsystems with distinct intrinsic oscillation frequencies will naturally mix, and support luxuriant stable and collective oscillatory behavior. We identify a dynamical phase characterized by quasi-periodic oscillations with multiple incommensurate frequencies, corresponding to a continuous-time quasi-crystalline order. In addition, we identify a phase transition from a time quasi-crystalline phase to a time-crystalline phase at sufficiently strong inter-chain coupling. This transition can be understood as the evolution from partially synchronized oscillations between the two chains to fully synchronized dynamics. From a mathematical perspective, we confirm that the transition is governed by either a saddle-node or a torus bifurcation, depending on the separation between the two original oscillation frequencies. These theoretical results provide guidance for exploring complex periodic dynamics in Rydberg atomic platforms.
The search for exotic temporal orders in quantum matter, such as discrete quasi-time crystals (DQTCs), has become an important theme in nonequilibrium physics. However, realizing these phases has so far required complex protocols, such as drives with multiple incommensurate frequencies. Here, we present a significantly simpler mechanism: the emergence of DQTCs in a dissipative collective spin system subjected to only a single periodic drive. Remarkably, the characteristic frequencies of this novel phase are not fixed but can be continuously tuned by varying the strength of the drive. Even more strikingly, this tunability is punctuated by Arnold tongues, within which the response main frequency locks to rational fractions of the drive. Our model further provides a unified framework that also encompasses stationary, discrete time crystals and chaotic phases. This discovery simplifies the requirements for generating complex temporal orders and opens a viable route towards the experimental control and manipulation of quasi-time crystalline matter.