Abstract
The notion of spontaneous symmetry breaking has been well established to characterize classical and quantum phase transitions of matter, such as condensation, crystallization or quantum magnetism. Generalizations of this paradigm to the time dimension can lead to a time crystal phase, which spontaneously breaks the time-translation symmetry of the system. Although the existence of a continuous time crystal at equilibrium has been challenged by no-go theorems, this difficulty can be circumvented by dissipation in an open system. Here we report the experimental observation of such a dissipative time-crystalline order in a room-temperature atomic gas, where ground-state atoms are continuously driven to Rydberg states. The emergent time crystal is revealed by persistent oscillations of the photon transmission, and we show that the observed limit cycles arise from the coexistence and competition between distinct Rydberg components. The non-decaying autocorrelation of the oscillation, together with the robustness against temporal noises, indicates the establishment of true long-range temporal order and demonstrates the realization of a continuous time crystal.
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Acknowledgements
We acknowledge valuable discussions with K. Mølmer, S. Hofferberth, Y. **ao, Y. Chen, F. Chen, Y. Tang, H. Yarloo and H. Zhang, as well as support from L. Yang. This work is supported by the National Natural Science Foundation of China (NSFC) (grant nos 92265205 and 12361131576), the Innovation Program for Quantum Science and Technology (2021ZD0302100) and National Key R&D Program of China (grant nos 2018YFA0306504 and 2018YFA0306503). L.Y. also acknowledges the support from the ‘Gravitational Wave Detection’ program (2023YFC2205800) funded by the National Natural Science Foundation of China. F.Y. and T.P. acknowledge support from the Carlsberg Foundation through the ‘Semper Ardens’ Research Project QCooL and from the Danish National Research Foundation (DNRF) through the Center of Excellence ‘CCQ’ (grant no. DNRF156). T.P. acknowledges support from the Austrian Science Fund (FWF) (10.55776/COE1) and the European Union—NextGenerationEU, and the Horizon Europe ERC synergy grant SuperWave (grant no. 101071882).
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X.W. constructed the initial experimental setup and observed the primary phenomenon, whereas Z.W. and X.L. gave crucial assistance. Z.W., R.G. and X.W. performed the experiments and analysed the data after thorough discussions with F.Y. The theoretical model was proposed by X.W., Z.W., F.Y. and T.P. The theoretical analysis and numerical simulations are conducted by F.Y. All authors discussed the results and contributed to the manuscript. X.L., T.P. and L.Y. supervised the study.
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Extended data
Extended Data Fig. 1 Mean-field dynamics.
The calculations are performed with Ω = 3γ, χ = − 16γ, and δ = 8γ. For the limit cycle phase shown in a with Δ = − 3γ, the order parameters exhibit persistent oscillations. For the stationary phase shown in b with Δ = 3γ, the order parameters converge to steady-state values.
Extended Data Fig. 2 Comparison between experiment and theory.
a Experimentally extracted oscillation frequency as a function of the effective two-photon Rabi frequency Ωeff = ΩcΩp/2Δp. In the experiment, we only vary the intensity of the coupling field (Ωc), and keep all other conditions the same as in Fig. 2d. b Theoretically predicted oscillation frequency as a function of the Rabi frequency Ω. The parameters chosen are close to the experiment. For example, the decay rate is evaluated to be γ/2π = 18.0 kHz, consisting of the contribution from the Rydberg spontaneous decay (γd) and the transient time broadening \({\gamma }_{t}={\bar{v}}_{\perp }/D\) with D the diameter of the beam and \({\bar{v}}_{\perp }=\sqrt{\pi kT/2m}\) the transverse mean velocity. The other parameters δ/2π = 0.306 MHz, Δ/2π = − 0.186 MHz, and χ/2π = − 0.951 MHz are also typical in our experiment.
Extended Data Fig. 3 A detailed schematic diagram of the experimental setup.
The 780 nm probe and reference beams generated from a calcite beam displacer are propagating in parallel through a room-temperature Rb vapor cell, with the probe beam overlap** with a counterpropagating coupling beam. Their transmission signals are detected on a balanced photon detector (PD) for differential measurement. The output intensity of the 780 nm laser from the fiber (monitored by an independent PD) is controlled by an AOM, whose RF driving is modulated by a waveform generator. QWPs are used to control the polarization of the lasers illuminating the atoms.
Extended Data Fig. 4 Transmission spectrum at different principal quantum number n.
a Oscillations do not occur at relatively low n. b-d As n increases, \(\left\vert n{D}_{3/2}\right\rangle\) and \(\left\vert n{D}_{5/2}\right\rangle\) states move closer, and their corresponding transmission peaks begin to merge. Oscillation appears and is enhanced for a sufficiently large n.
Extended Data Fig. 5 Long-term stability of the oscillation frequency and breaking of continuous time translation symmetry.
a The long-term frequency drift in 200 independent realizations of the quench dynamics by extracting peak frequencies in the stable periodic region (50-100 ms). The data encircled by the red box are of the same frequency, and are postselected for b, which displays the distribution of the Fourier amplitudes (at the same peak frequency) on the complex plane. c Single-shot and average transmission signals over 36 realizations with a same stable frequency indicated by the red box in a.
Extended Data Fig. 6 Fluorescence measurements in our Rydberg gas.
a and d are transmission signals at different principal quantum number n = 55 and n = 75, respectively. Red squares represent the counts of 780 nm phontons collected by the spectrometer. b-c and e-f show the full spectra from 200 nm to 1000 nm at different dutunings indicated in a and d.
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Wu, X., Wang, Z., Yang, F. et al. Dissipative time crystal in a strongly interacting Rydberg gas. Nat. Phys. (2024). https://doi.org/10.1038/s41567-024-02542-9
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DOI: https://doi.org/10.1038/s41567-024-02542-9
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