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Physical Review A

Emergent synchronization mode in coupled Rydberg atomic chains

Weilun Jiang

Published Nov 12, 2025• 0 citations
Publisher

Abstract

We report an oscillatory form in the two coupled dissipative Rydberg atomic chains by modulating its spacing. Such oscillation has $\ensuremath{\pi}$-phase difference between two neighboring sites, which distinguishes it from antiferromagnetic-type synchronization in the previous studies. Theoretically, we find a phase with two coexisting types of continuous time crystals and recognize that the transition belongs to Hopf and pitchfork bifurcation. Furthermore, we generalize the conclusion to multiple chains and verify the uniqueness of the synchronization mode. We also discuss its experimental feasibility.

DOI
10.1103/87jf-zj5g

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Acta Physica Sinica•Jan 1, 2025•0 citations
We report an oscillatory form in the two coupled dissipative Rydberg atomic chains by modulating its spacing. Such oscillation has \ensuremathπ\ensuremath{\pi}\ensuremathπ-phase difference between two neighboring sites, which distinguishes it from antiferromagnetic-type synchronization in the previous studies. Theoretically, we find a phase with two coexisting types of continuous time crystals and recognize that the transition belongs to Hopf and pitchfork bifurcation. Furthermore, we generalize the conclusion to multiple chains and verify the uniqueness of the synchronization mode. We also discuss its experimental feasibility.
We report a new oscillatory form in the two coupled dissipative Rydberg atomic chains by modulating its spacing. Such oscillation has πππ-phase difference between two neighboring sites, which distinguishes itself from antiferromagnetic-type synchronization in the previous studies. Theoretically, we find a phase with coexisting two types of continuous time crystals, and recognize that the transition belongs to Hopf and pitchfork bifurcation. Furthermore, we generalize the conclusion to multiple chains and verify the uniqueness of the new synchronization mode. We also discuss its experimental feasibility.
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.
A time crystal is an exotic phase of matter where time-translational symmetry is broken; this phase differs from the spatial symmetry breaking induced in conventional crystals. Lots of experiments report the transition from a thermal equilibrium phase to a time crystal phase. However, there is no experimental method to probe the bifurcation effect of distinct continuous time crystals in quantum many-body systems. Here, in a driven and dissipative many-body Rydberg atom system, we observe multiple continuous dissipative time crystals and emergence of more complex temporal symmetries beyond the single time crystal phase. Bifurcation of time crystals in strongly interacting Rydberg atoms is observed; the process manifests as a transition from a time crystal of long periodicity to a time crystal of short periodicity, or vice versa. By manipulating the driving field parameters, we observe the time crystal’s bistability and a hysteresis loop. These investigations indicate new possibilities for control and manipulation of the temporal symmetries of non-equilibrium systems. The time crystal is an exotic phase of matter where time-translational symmetry is broken. Here, the authors observe multiple continuous dissipative time crystals and bifurcation of time crystals in driven and dissipative Rydberg atomic gas.
A time crystal is an exotic phase of matter where time-translational symmetry is broken; this phase differs from the spatial symmetry breaking induced in crystals in space. Lots of experiments report the transition from a thermal equilibrium phase to time crystal phase. However, there is no experimental method to probe the bifurcation effect of distinct time crystals in quantum many-body systems. Here, in a driven and dissipative many-body Rydberg atom system, we observe multiple continuous dissipative time crystals and emergence of more complex temporal symmetries beyond the single time crystal phase. Bifurcation of time crystals in strongly interacting Rydberg atoms is observed; the process manifests as a transition from a time crystal state of long temporal order to one of short temporal order, or vice versa. By manipulating the driving field parameters, we observe the time crystal's bistability and a hysteresis loop. These investigations indicate new possibilities for control and manipulation of the temporal symmetries of non-equilibrium systems.
We study a driven-dissipative system of atoms in the presence of laser excitation to a Rydberg state and spontaneous emission. The atoms interact via the blockade effect, whereby an atom in the Rydberg state shifts the Rydberg level of neighboring atoms. We use mean-field theory to study how the Rydberg population varies in space. As the laser frequency changes, there is a continuous transition between the uniform and antiferromagnetic phases. The nonequilibrium nature also leads to a novel oscillatory phase and bistability between the uniform and antiferromagnetic phases.
This work investigates nonequilibrium phase transitions in a Rydberg atomic system under collective dissipation. By combining mean-field theory and Liouvillian spectral analysis, we reveal novel nonequilibrium phases induced by collective dissipation and compare the results from both approaches. Our findings indicate that collective dissipation not only generates interatomic correlations but also sustains persistent periodic oscillations and a unique bistable form, in which the system may evolve to a steady state or sustain self-consistent oscillatory dynamics. This study highlights the rich nonequilibrium phenomena present in quantum many-body systems and provides an extensible spectral framework for exploring dissipative phases in Rydberg and related systems. Recent experiments have reported persistent oscillations in thermal Rydberg atomic ensembles, yet the theoretical consensus on their origin remains elusive. Motivated by these observations, we introduce a collective dissipation mechanism and employ both mean-field approximations and the Liouvillian spectrum method to systematically explore nonequilibrium phase transitions. Our results show that the collective dissipation effectively induces interatomic correlations and sustains persistent periodic oscillations, in which under the same parameters, independent dissipation leads the system to relax to a stationary state. Furthermore, the nonlinear effects arising from collective dissipation give rise to a novel type of bistability, in which the system can converge to a fixed point or maintain self-consistent periodic oscillations. This mechanism is clearly different from the traditional bistability induced by Rydberg interactions, which involves two steady states. Moreover, the Liouvillian spectral method, based on the quantum master equation, successfully captures the features of nonequilibrium phase transitions even in finite-dimensional systems, and the results accord well with those obtained from mean-field approximation in the thermodynamic limit. Our work not only provides a theoretical explanation for recently observed oscillatory phenomena but also predicts novel bistable states and rich nonequilibrium phase structures. It further verifies the effectiveness of the Liouvillian spectroscopic method in studying quantum many-body systems, making significant contributions to understanding the microscopic mechanisms underlying nonequilibrium phase transitions.