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arXiv:2603.12170 · Physical Review Research

Frequency Comb Behavior of Time Crystals in an RF-Driven Dissipative Rydberg System

Dixith Manchaiah, William J. Watterson, Christopher L. Holloway

physics.atom-phquant-phSubmitted Mar 12, 2026• Announced Mar 13, 2026• 0 citations
arXivHTMLPDF

Abstract

Driven nonlinear oscillators constitute a universal paradigm for understanding synchronization, frequency pulling, and frequency comb formation in nonequilibrium systems. Here, we realize such an emergent nonlinear oscillator in strongly interacting cesium Rydberg vapor, where coherent optical excitation, dissipation, and long-range interactions give rise to a driven-dissipative time crystal phase with intrinsic oscillation frequencies. Applying a radio-frequency (RF) field allows controlled tuning of the intrinsic oscillation frequency. Under RF heterodyne conditions, we observe intermodulation, frequency pulling, and, at strong drive, the emergence of a comb-like spectrum in the atomic coherence. We quantitatively capture these observations using a four-level mean-field model and demonstrate a classical analogue with a driven Van der Pol oscillator. Our results establish interacting Rydberg ensembles as a tunable platform for exploring nonequilibrium time-crystalline order, nonlinear synchronization, and frequency comb generation in many-body atomic systems.

Journal reference
Phys. Rev. Research 8, 033115,2026
DOI
10.1103/fg8f-q4rs
Comments
14Pages, 7 figures

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Driven nonlinear oscillators constitute a universal paradigm for understanding synchronization, frequency pulling, and frequency comb formation in nonequilibrium systems. Here, we realize such an emergent nonlinear oscillator in strongly interacting cesium Rydberg vapor, where coherent optical excitation, dissipation, and long-range interactions give rise to a driven-dissipative time crystal phase with intrinsic oscillation frequencies. Applying a radio-frequency (RF) field allows controlled tuning of the intrinsic oscillation frequency. Under RF heterodyne conditions, we observe intermodulation, frequency pulling, and, at strong drive, the emergence of a comb-like spectrum in the atomic coherence. We quantitatively capture these observations using a four-level mean-field model and demonstrate a classical analogue with a driven Van der Pol oscillator. Our results establish interacting Rydberg ensembles as a tunable platform for exploring nonequilibrium time-crystalline order, nonlinear synchronization, and frequency comb generation in many-body atomic systems.
Non-equilibrium Rydberg gases exhibit exotic many-body phases stabilized by the interplay of coherent interactions and dissipation. Strong Rydberg interactions drive sustained limit cycle oscillations, whose robustness, long-range temporal order, and spontaneous time-translation symmetry breaking establish a dissipative time crystal (DTC). Collective self-entrainment in driven ensembles leads to global synchronization and a dominant oscillation frequency. Here, injection locking of a Rydberg DTC is demonstrated using a radio-frequency (RF) electric field that gradually pulls the intrinsic oscillation toward the injected frequency. Above a critical threshold, full synchronization occurs, with the locking bandwidth scaling linearly with RF amplitude. This includes synchronization of higher-order harmonics, revealing entrainment of the system’s nonlinear temporal dynamics. The phenomenon parallels injection locking in classical nonlinear systems, but emerges here in a strongly interacting quantum medium. This approach establishes a new method for stabilizing and controlling time-crystalline temporal order, with applications in precision sensing, quantum metrology, and timekeeping. Non-equilibrium Rydberg gases exhibit unique many-body phases arising from the interplay of coherent interactions and dissipation, yet controlling their temporal order remains challenging. This work demonstrates injection locking of a Rydberg dissipative time crystal using a radio-frequency electric field, achieving full synchronization and revealing dynamical behavior relevant to precision sensing and quantum metrology.
Non-equilibrium Rydberg gases exhibit exotic many-body phases stabilized by the interplay of coherent interactions and dissipation. Strong Rydberg interactions drive sustained limit cycle oscillations, whose robustness, long-range temporal order, and spontaneous time-translation symmetry breaking establish a dissipative time crystal (DTC). Collective self-entrainment in driven ensembles leads to global synchronization and a dominant oscillation frequency. Here, injection locking of a Rydberg DTC is demonstrated using a radio-frequency (RF) electric field that gradually pulls the intrinsic oscillation toward the injected frequency. Above a critical threshold, full synchronization occurs, with the locking bandwidth scaling linearly with RF amplitude. This includes synchronization of higher-order harmonics, revealing entrainment of the system's nonlinear temporal dynamics. The phenomenon parallels injection locking in classical nonlinear systems, but emerges here in a strongly interacting quantum medium. This approach establishes a new method for stabilizing and controlling time-crystalline temporal order, with applications in precision sensing, quantum metrology, and timekeeping.
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 Moiré time crystal is a non-equilibrium quantum phase emerging from the coherent interference of two distinct frequencies, at least one being the intrinsic oscillation of a symmetry-broken time crystal. Its hallmark is an ultra-long beat period, reflecting a time-domain mapping of the Moiré fringes that arise from mismatched spatial lattices. However, to date, no experimental realization of such a Moiré time crystal has been reported. In this work, by applying a bichromatic driving field with two distinct frequencies, we demonstrate that the interplay between long-range Rydberg interactions and dissipation gives rise to a unique comb-like Moiré pattern characterized by a beat-note comb, which superimposes subharmonic periodicity and fundamental frequencies. This Moiré pattern formed by two mismatched drives is staggered in the spectrum as the frequency of one driver changes. We experimentally map the phase diagram of the system and identify a robust region where the Moiré temporal order persists against perturbations in laser detuning. The reported Moiré time crystal not only provides a controllable platform for exploring emergent slow-fast dynamics and synthetic space-time symmetries but also opens avenues for engineering complex temporal order in driven quantum many-body systems.
Time crystals are a unique and recently discovered state of matter in which time-translational symmetry is spontaneously broken. Although this state has been observed across a variety of quantum systems, understanding the nature between driving, dissipation, and noise and the effects of these forces on the state lifetime remains elusive. Here, we study phase diffusion and entrainment of the time crystalline oscillatory state of a thermal-vapor Rydberg atom ensemble. We apply a pulsed rf heterodyne driving field which can entrain the oscillation frequency during the on driving period. During the off period, the entrained ensemble phase diffuses on a 1/eee timescale up to 2.3 ms -- significantly longer than the Rydberg state lifetime. We additionally study how the entrainment and phase diffusion timescales are affected by the strength and detuning of the rf driving field, and develop a classical Fokker-Planck model with an Adler-based driving term that reproduces the observed experimental findings. These results demonstrate the creation of a long-time synchronized time crystal Rydberg atom ensemble state, which could be utilized in applications requiring frequency and phase stability.
Time crystals, as temporal analogs of space crystals, manifest as stable and periodic behavior that breaks time translation symmetry. In an open quantum system, many-body interaction subjected to dissipation allows one to develop the time crystalline order in an unprecedented way, as refer to dissipative time crystals. Here we report the observation of multiple time crystals in the continuously driven-dissipative and strongly interacting Rydberg thermal gases, in which continuous time crystals, sub-harmonic time crystals and high-harmonic time crystals are observed in the same system by manipulating the Rydberg excitation. Our work provides new ways to explore the non-equilibrium phases of matter in open systems. Such time crystals with persistent oscillation rooted in emergent quantum correlations, may emerge as a ubiquitous tool in quantum metrology, for instance, continuous sensing and parameter estimation surpassing the standard quantum limit. The authors observed multiple time crystals in the continuously driven-dissipative and strongly interacting Rydberg thermal gases. This discovery may benefit the field of quantum metrology, such as continuous sensing, potentially surpassing the standard quantum limit, and time crystalline order as a frequency standard.