- Open Access
Frequency comb behavior of time crystals in an rf-driven dissipative Rydberg system
Phys. Rev. Research 8, 033115 – Published 27 July, 2026
DOI: https://doi.org/10.1103/fg8f-q4rs
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 intermodulations, frequency pulling, and, at strong drive, the emergence of a comblike spectrum in the atomic coherence. We qualitatively capture these observations using a four-level mean-field model and demonstrate a classical analog 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.
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References (35)
- F. Wilczek, Quantum time crystals, Phys. Rev. Lett. 109, 160401 (2012).
- A. Shapere and F. Wilczek, Classical time crystals, Phys. Rev. Lett. 109, 160402 (2012).
- K. Sacha and J. Zakrzewski, Time crystals: A review, Rep. Prog. Phys. 81, 016401 (2018).
- S. Choi, J. Choi, R. Landig, G. Kucsko, H. Zhou, J. Isoya, F. Jelezko, S. Onoda, H. Sumiya, V. Khemani, C. von Keyserlingk, N. Y. Yao, E. Demler, and M. D. Lukin, Observation of discrete time-crystalline order in a disordered dipolar many-body system, Nature (London) 543, 221 (2017).
- J. Zhang et al., Observation of a discrete time crystal, Nature (London) 543, 217 (2017).
- W. W. Ho, S. Choi, M. D. Lukin, and D. A. Abanin, Critical time crystals in dipolar systems, Phys. Rev. Lett. 119, 010602 (2017).
- D. Dreon, A. Baumgärtner, X. Li, S. Hertlein, T. Esslinger, and T. Donner, Self-oscillating pump in a topological dissipative atom–cavity system, Nature (London) 608, 494 (2022).
- H. Keßler, P. Kongkhambut, C. Georges, L. Mathey, J. G. Cosme, and A. Hemmerich, Observation of a dissipative time crystal, Phys. Rev. Lett. 127, 043602 (2021).
- B. Zhu, J. Marino, N. Y. Yao, M. D. Lukin, and E. A. Demler, Dicke time crystals in driven-dissipative quantum many-body systems, New J. Phys. 21, 073028 (2019).
- K. Wadenpfuhl and C. S. Adams, Emergence of synchronization in a driven-dissipative hot Rydberg vapor, Phys. Rev. Lett. 131, 143002 (2023).
- V.-T. Pham, S. Vaidyanathan, and T. Kapitaniak, Complexity, dynamics, control, and applications of nonlinear systems with multistability, Complexity 2020, 8510930 (2020).
- S. H. Strogatz, From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators, Physica D 143, 1 (2000).
- J. A. Acebrón, L. L. Bonilla, C. J. Pérez Vicente, F. Ritort, and R. Spigler, The Kuramoto model: A simple paradigm for synchronization phenomena, Rev. Mod. Phys. 77, 137 (2005).
- N. Šibalić, C. G. Wade, C. S. Adams, K. J. Weatherill, and T. Pohl, Driven-dissipative many-body systems with mixed power-law interactions: Bistabilities and temperature-driven nonequilibrium phase transitions, Phys. Rev. A 94, 011401 (2016).
- A. W. Glaetzle, R. Nath, B. Zhao, G. Pupillo, and P. Zoller, Driven-dissipative dynamics of a strongly interacting Rydberg gas, Phys. Rev. A 86, 043403 (2012).
- X. Wu, Z. Wang, F. Yang, R. Gao, C. Liang, M. K. Tey, X. Li, T. Pohl, and L. You, Dissipative time crystal in a strongly interacting Rydberg gas, Nat. Phys. 20, 1389 (2024).
- C. Carr, R. Ritter, C. G. Wade, C. S. Adams, and K. J. Weatherill, Nonequilibrium phase transition in a dilute Rydberg ensemble, Phys. Rev. Lett. 111, 113901 (2013).
- D.-S. Ding, H. Busche, B.-S. Shi, G.-C. Guo, and C. S. Adams, Phase diagram and self-organizing dynamics in a thermal ensemble of strongly interacting Rydberg atoms, Phys. Rev. X 10, 021023 (2020).
- D. Ding, Z. Bai, Z. Liu, B. Shi, G. Guo, W. Li, and C. S. Adams, Ergodicity breaking from Rydberg clusters in a driven-dissipative many-body system, Sci. Adv. 10, adl5893 (2024).
- B. Liu et al., Bifurcation of time crystals in driven and dissipative Rydberg atomic gas, Nat. Commun. 16, 1419 (2025).
- Y. Jiao, W. Jiang, Y. Zhang, J. Bai, Y. He, H. Shen, J. Zhao, and S. Jia, Observation of multiple time crystals in a driven-dissipative system with Rydberg gas, Nat. Commun. 16, 8767 (2025).
- B. Liu, L.-H. Zhang, Q.-F. Wang, Y. Ma, T.-Y. Han, J. Zhang, Z.-Y. Zhang, S.-Y. Shao, Q. Li, H.-C. Chen, B.-S. Shi, and D.-S. Ding, Higher-order and fractional discrete time crystals in Floquet-driven Rydberg atoms, Nat. Commun. 15, 9730 (2024).
- Y. Jiao, Y. Zhang, J. Bai, S. Jia, C. S. Adams, Z. Bai, H. Shen, and J. Zhao, Photoionization-induced Floquet driving of a discrete time crystal in a thermal Rydberg ensemble, Phys. Rev. Lett. 135, 163603 (2025).
- D. Arumugam, Electric-field sensing with driven-dissipative time crystals in room-temperature Rydberg vapor, Sci. Rep. 15, 13446 (2025).
- D. Arumugam, Stark modulated Rydberg dissipative time crystals at room temperature applied to sub-kHz electric field sensing, Sci. Rep. 15, 35976 (2025).
- D. Arumugam and B. Feyissa, Stabilization of Rydberg dissipative time crystals using a scanning Fabry–Pérot interferometer transfer lock, Appl. Phys. Lett. 128, 104002 (2026).
- D. Arumugam, Fizeau wavemeter stabilized Rydberg dissipative time crystals, Opt. Continuum 5, 595 (2026).
- M. T. Simons, A. H. Haddab, J. A. Gordon, and C. L. Holloway, A Rydberg atom-based mixer: Measuring the phase of a radio frequency wave, Appl. Phys. Lett. 114, 114101 (2019).
- D. Arumugam, Injection locking of Rydberg dissipative time crystals, Commun Phys 9, 156 (2026).
- C. L. Holloway, M. T. Simons, J. A. Gordon, A. Dienstfrey, D. A. Anderson, and G. Raithel, Electric field metrology for SI traceability: Systematic measurement uncertainties in electromagnetically induced transparency in atomic vapor, J. Appl. Phys. 121, 233106 (2017).
- S. Strogatz, Nonlinear Dynamics and Chaos (Addison-Wesley, Reading, MA, 1994).
- J. D. Cook, Driven Van der Pol oscillators, https://www.johndcook.com/blog/2019/12/26/driven-van-der-pol.
- L. S. Cao, D. X. Qi, R. W. Peng, M. Wang, and P. Schmelcher, Phononic frequency combs through nonlinear resonances, Phys. Rev. Lett. 112, 075505 (2014).
- J. S. Ochs, D. K. J. Boneß, G. Rastelli, M. Seitner, W. Belzig, M. I. Dykman, and E. M. Weig, Frequency comb from a single driven nonlinear nanomechanical mode, Phys. Rev. X 12, 041019 (2022).
- https://doi.org/10.18434/mds2-4131.