Microwave power-to-frequency transduction is demonstrated using the emergent oscillation frequency of a magnetically initiated Rydberg dissipative time crystal (DTC). In a room-temperature 87Rb vapor, a ~14 G magnetic field establishes a self-sustained DTC near 21 kHz, while a near-resonant 8.325 GHz field coupling the 63D3/2 to 64P3/2 manifold continuously shifts the autonomous oscillation frequency. The resulting field-to-frequency transfer function is strongly nonlinear, with a total fundamental-frequency excursion of ~6.7 kHz and peak responsivity approaching 1 kHz/(mV/cm). The nonlinear transition is substantially steeper than a simple quadratic saturation response and is captured by a self-consistent mean-field picture in which microwave-driven Rydberg-population redistribution modifies the collective resonance condition. Higher DTC harmonics preserve the same normalized transfer function while exhibiting approximately linear growth of absolute responsivity with harmonic order. These results establish an intrinsic many-body atomic route to RF amplitude-to-frequency conversion, enabling continuous frequency-domain sensing through an emergent atomic frequency without an externally engineered RF feedback oscillator, repeated optical spectral scans, or resolved Autler Townes splitting.
Microwave power-to-frequency transduction is demonstrated using the emergent oscillation frequency of a magnetically initiated Rydberg dissipative time crystal (DTC). In a room-temperature 87Rb vapor, a ~14 G magnetic field establishes a self-sustained DTC near 21 kHz, while a near-resonant 8.325 GHz field coupling the 63D3/2 to 64P3/2 manifold continuously shifts the autonomous oscillation frequency. The resulting field-to-frequency transfer function is strongly nonlinear, with a total fundamental-frequency excursion of ~6.7 kHz and peak responsivity approaching 1 kHz/(mV/cm). The nonlinear transition is substantially steeper than a simple quadratic saturation response and is captured by a self-consistent mean-field picture in which microwave-driven Rydberg-population redistribution modifies the collective resonance condition. Higher DTC harmonics preserve the same normalized transfer function while exhibiting approximately linear growth of absolute responsivity with harmonic order. These results establish an intrinsic many-body atomic route to RF amplitude-to-frequency conversion, enabling continuous frequency-domain sensing through an emergent atomic frequency without an externally engineered RF feedback oscillator, repeated optical spectral scans, or resolved Autler Townes splitting.
A Rydberg superheterodyne sensing architecture is demonstrated in which a self-sustained oscillator (SSO) serves as a dynamically perturbed local oscillator (LO) for microwave detection. The SSO is realized by a phase-controlled radio-frequency (RF) feedback loop coupled to a transverse electromagnetic (TEM) cavity containing a Rydberg vapor cell. The system operates near 5.49 GHz using a cesium ladder scheme with an 852 nm probe and 510 nm coupling laser addressing the 6S to 6P to 49D transition, with microwave coupling to the 50P state. Injection of a microwave signal pulls the SSO frequency via nonlinear dynamics, converting input power into a measurable frequency shift read out optically as a Rydberg probe intermediate-frequency (IF) signal. The response follows Adler-type injection-pulling behavior, with continuous IF tuning with input power. A peak responsivity of 35 kHz/dB is observed, with enhanced sensitivity near synchronization. These results demonstrate power-to-frequency transduction using a dynamically perturbed LO combined with Rydberg atomic readout.
Out-of-equilibrium Rydberg gases exhibit emergent many-body phases due to mode competition. Sustained limit cycle oscillations (OSC) emerge when driven by B-fields at room-temperature, forming robust Rydberg dissipative time crystals (DTC). These driven-dissipative Rydberg DTC have recently been shown to develop an effective transition centered at the OSC frequency (-10dB bandwidth of ~1.7kHz, centered at 9.8kHz). Weak RF signals injected within this emergent transition perturb and emerge on the OSC spectrum, from which sensitive and high-resolution sensing of E-fields (~1.6-2.3 uVcm-1Hz-1/2) near the OSC frequencies can be achieved. In this article, it is demonstrated that DC and AC Stark fields in the sub-kHz regime can be used effectively to shift (DC) or modulate (AC) the OSC frequency of Rydberg DTC at room-temperature. The AC-Stark driven modulation of the OSC is shown as an effective technique to sense weak AC E-fields in the sub-kHz regime. With a modest setup, a sensitivity of ~7.8 uVcm-1Hz-1/2 for AC signals at 300Hz (~8.7x improvement over state-of-art Rydberg atom techniques), and high-resolution detection to as low as sub-Hz is demonstrated. This approach enables the development of ultra-compact, extremely low-frequency E-field detectors for applications in remote sensing, communications, navigation, and bio-medical technologies.
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 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.
Out-of-equilibrium Rydberg gases exhibit emergent many-body phases due to mode competition. Sustained limit cycle oscillations (OSC) emerge when driven by B-fields at room temperature, forming robust Rydberg dissipative time crystals (DTC). Here we show that DC and AC Stark fields in the sub-kHz regime can be used to precisely shift (DC) or modulate (AC) the oscillation frequency of these DTCs, providing a powerful method for controllable time-domain dynamics in a room-temperature system. The AC Stark modulation induces frequency modulation (FM) of the OSC spectrum, enabling narrowband detection of extremely weak AC electric fields in the sub-kHz regime, with DC fields detected via Stark-induced shifts of the oscillation frequency. With a modest setup, a sensitivity of ~ 7.8µVcm − 1 Hz − 1/2 at 300 Hz is demonstrated — an ~ 8.7× improvement over state-of-art in the sub-kHz regime. Unlike on-resonant DTC sensing that is limited to operation close to the emergent limit cycle oscillations (10–15 kHz), the present approach is effective in the DC-600 Hz sub-kHz regime. This approach overcomes the size and bandwidth limitations of classical antennas at ultra-low frequencies and establishes a new class of ultra-compact ( ≪ λ/10⁶) Rydberg-based electric-field sensors. These results open opportunities for compact extremely low-frequency (ELF) sensors in remote sensing, communications, geophysics, and biomedical diagnostics.
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.