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

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.

Figures (7)

• Figure 1: (a) Energy-level diagram of the four-level cesium system driven by optical and RF fields. (b) Experimental setup for two-photon excitation of cesium atoms. The probe laser is shown in red and coupling laser is shown in teal, counter-propagates with respect to each other. The rf signal and LO fields are applied using a horn antenna. M1, M2: mirrors; DM: dichroic mirror; PD: photodetector; SA: spectrum analyzer; Signal+LO: combined rf signal and LO fields.
• Figure 2: (a) Probe transmission as a function of the coupling detuning for different coupling Rabi frequencies. (b) Time domain probe transmission for different coupling laser detunings, showing the emergence of self-sustained oscillations. (c) Frequency domain spectrum of the time domain signal corresponding to $\Delta_c$ = 10 MHz shown in Fig. \ref{['fig:1']}b measured using a spectrum analyzer.
• Figure 3: (a) Two dimensional color map of the RF power as a function of frequency, showing the evolution of the oscillation frequency with increasing RF drive strength. (b) Intermodulation products and injection locking of the stable oscillation phase mixing with the RF heterodyne beatnote. The stable oscillation phase has a main component near 10 kHz and a harmonic at 20 kHz. The primary beatnotes are indicated by the legend and the mixed products occur at the sum and difference frequencies between the beatnote and stable oscillations. The traces are offset vertically for clarity with a similar noise floor of -120 dBm for each trace. (c) Two dimensional color map measured under heterodyne conditions, showing the signal amplitude as a function of frequency and RF power. The LO power is fixed at 0 dBm, and detuned by 10 kHz from RF signal field.
• Figure 4: (a) Frequency comb-like structure in the heterodyne spectrum for a LO RF power of 0 dBm and a signal RF power of 5 dBm. (b) Peak frequency versus comb tooth index. The data points are fitted to the frequency comb equation (solid line). The inset shows the frequency spacing between adjacent teeth, and the bottom panel shows the residuals versus tooth index.
• Figure 5: Velocity-resolved Rydberg state population as a function of time for $V_{\mathrm{norm}} = 400$, $\beta = 2.3$, $\Omega_p/\Gamma_{21} = 6~\mathrm{MHz}$, and $\Omega_c/\Gamma_{21} = 5~\mathrm{MHz}$.