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Physical Review X

Ultralow-Power Microwave Frequency Comb at a Bistable Phase Transition

Hanfeng Wang, Kurt A. Jacobs, Dirk Englund, Matthew E. Trusheim

Published Jan 29, 2026• 2 citations
Publisher

Abstract

Nonlinear phenomena underpin a broad array of technologies, from electronic frequency mixers and harmonic generation to parametric amplification and optical frequency doubling. Conventional schemes for generating microwave frequency combs are constrained by intrinsic material or junction properties that require high driving powers. Here, we overcome these limitations via phase-transition physics. We show that a hybrid quantum system—composed of a solid-state spin ensemble and a nonlinear oscillator—exhibits a distinct bistable phase transition point (BP) where system response becomes both highly enhanced and nonlinear. The nonlinearity around the BP is higher order than other phase transitions, such as exceptional points, critically producing high-order frequency response which enhances nonlinear processes. Approaching the BP, we demonstrate a frequency comb with a record number of teeth at unprecedentedly low driving powers, surpassing previous results using magnonic systems and traditional diode-based approaches. These findings highlight the potential of hybrid quantum systems in advancing high-performance frequency manipulation.

DOI
10.1103/59xl-zyxp

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Nonlinear phenomena underpin a broad array of technologies, from electronic frequency mixers and harmonic generation to parametric amplification and optical frequency doubling. Conventional schemes for generating microwave frequency combs are constrained by intrinsic material or junction properties that require high driving powers. Here, we overcome these limitations via phase-transition physics. We show that a hybrid quantum system—composed of a solid-state spin ensemble and a nonlinear oscillator—exhibits a distinct bistable phase transition point (BP) where system response becomes both highly enhanced and nonlinear. The nonlinearity around the BP is higher order than other phase transitions, such as exceptional points, critically producing high-order frequency response which enhances nonlinear processes. Approaching the BP, we demonstrate a frequency comb with a record number of teeth at unprecedentedly low driving powers, surpassing previous results using magnonic systems and traditional diode-based approaches. These findings highlight the potential of hybrid quantum systems in advancing high-performance frequency manipulation.
We investigate the dynamics of a microwave-driven Josephson junction capacitively coupled to a lumped-element LC oscillator. In the regime of driving where the Josephson junction can be approximated as a Kerr oscillator, this minimal nonlinear system has been previously shown to exhibit a bistability in phase and amplitude. In the present study, we characterize the full phase diagram and show that besides a parameter regime exhibiting bistability, there is also a regime of self-oscillations characterized by a frequency comb in its spectrum. We discuss the mechanism of comb generation which appears to be different from those studied in microcavity frequency combs and mode-locked lasers. We then address the fate of the comblike spectrum in the regime of strong quantum fluctuations, reached when nonlinearity becomes the dominant scale with respect to dissipation. We find that the nonlinearity responsible for the emergence of the frequency combs also leads to its dephasing, leading to broadening and ultimate disappearance of sharp spectral peaks. Our study explores the fundamental question of the impact of quantum fluctuations for quantum systems which do not possess a stable fixed point in the classical limit.
The efficient generation, coherent control, manipulation and measurement of quantum states of light and matter is at the core of quantum technologies. Hybrid quantum systems, where one combines the best parts of multiple individual quantum systems together without their weaknesses, are now seen as a way to engineer composite quantum systems with the properties one requires. This would in principle allow one to probe new physical regimes. However, the issue until recently has been that hybridization has not resulted in systems with superior properties. Recently however we [Nature Photonics 11, 3639 (2016)] have shown an increased coherence times in hybrid system is of composed nitrogen-vacancy centers strongly coupled to a superconducting microwave resonator. This demonstration has enabled this kind of hybrid system to enter the regime where quantum nonlinearities are present. We discuss several types of nonlinearity effects that can be naturally explored (bistability and superradiance). Our work paves the way for the creation of spin squeezed states, novel metamaterials, long-lived quantum multimode memories and solid-state microwave frequency combs. Further in the longer term it may enable the exploration of many-body phenomena in new cavity quantum electrodynamics experiments.
A scheme for realizing loss-induced enhancement of optical nonlinearity in a non-Hermitian cavity quantum electrodynamics system is proposed and investigated. It is shown that the system can experience an exceptional point (EP)-based phase transition process by varying the additional loss induced on the system, which leads to nontrivial phenomena with interesting counterintuitive features. We demonstrate that the Kerr nonlinearity in the system can be counterintuitively monotonically enhanced by increasing the additional loss, meanwhile, a high on-resonance linear transmission rate of the system can be maintained. Furthermore, we also demonstrate that the loss-induced nonlinearity enhancement is beneficial for realizing broadband and robust optical frequency comb. These results indicate that the additional loss can be utilized as an alternative degree of freedom to control the nonlinear dynamics of the system based on the EP-related features, which may be used in a variety of nonlinearity-based applications ranging from information processing to precision measurement.
Frequency combs represent exceptionally precise measurement tools due to the coherence of their spectral lines. While optical frequency comb sources constitute a well-established technology, superconducting circuits provide a relatively unexplored on-chip platform for low-dissipation comb emitters able to span from gigahertz to terahertz frequencies. We demonstrate coherent microwave frequency comb generation by leveraging the ac Josephson effect in a superconducting quantum interference device. A time-dependent magnetic drive periodically generates voltage pulses, which in the frequency domain correspond to a comb with dozens of spectral modes here reported up to mode 46. The emitted power at the device level ranges from -170 dBm to -130 dBm per harmonic, corresponding to 40 dB dynamic range in the 4-8 GHz bandwidth. The micrometer-scale footprint and minimal dissipation inherent to superconducting systems foster the integration of our comb generator with advanced cryogenic electronics. Transferring optical techniques to the solid-state domain may enable new applications in quantum technologies.
Based on a single atom coupled to a fiber-coupled, chip-based microresonator [B. Dayan et al., Science 319, 1062 (2008)], we put forward a scheme to generate optical frequency combs at driving laser powers as low as a few nanowatts. Using state-of-the-art experimental parameters, we investigate in detail the influences of different atomic positions and taper-resonator coupling regimes on optical-frequency-comb generation. In addition to numerical simulations demonstrating this effect, a physical explanation of the underlying mechanism is presented. We find that the combination of the atom and the resonator can induce a large third-order nonlinearity which is significantly stronger than Kerr nonlinearity in Kerr frequency combs. Such enhanced nonlinearity can be used to generate optical frequency combs if driven with two continuous-wave control and probe lasers and significantly reduce the threshold of nonlinear optical processes. The comb spacing can be well tuned by changing the frequency beating between the driving control and probe lasers. The proposed method is versatile and can be adopted to different types of resonators, such as microdisks, microspheres, microtoroids or microrings.
Optical-frequency combs consisting of equally spaced sharp lines in frequency space have triggered substantial advances in optical-frequency metrology and precision measurements and in applications such as laser-based gas sensing and molecular fingerprinting. Here, we propose a scheme to generate a type of optical-frequency combs and convert them from one cavity to the other in a hybrid optical system composed of a pair of coupled photonic crystal cavities called a photonic molecule (PM) and a single semiconductor quantum dot (QD) embedded in one cavity of the molecule. Optical-frequency combs are formed by the interaction between a cavity mode and a continuous-wave (CW) two-tone driving laser consisting of a pump field and a seed field via QD-induced strong nonlinearity. In this situation, the initial input pump and seed CW lasers can interact among each other and produce optical higher-order sidebands with equal spacing via parametric frequency conversion provided by QD-induced nonlinear optical effects. Using numerical simulations, it is clearly shown that the beat frequency of the two-tone components plays an important role in determining the comb spacing and matched frequency combs can be formed in the PM. We also demonstrate that the present interacting QD-PM system can serve as a platform to generate large-scale quantum entanglement between two comb modes. The results obtained here may be useful for real experiments in a photonic crystal platform.