Cavity optomechanics implements a unique platform where moving objects can be probed by quantum fields, either laser light or microwave signals. With a pump tone driving at a frequency above the cavity resonance, self-sustained oscillations can be triggered at large injected powers. These limit-cycle dynamics are particularly rich, presenting hysteretic behaviors, broad comb signals, and especially large motion amplitudes. All of these features can be exploited for both fundamental quantum research and engineering. Here we present low-temperature microwave experiments performed on a high- Q cavity resonance capacitively coupled to the flexure of a beam resonator. We study the limit-cycle dynamics parameter space as a function of pump parameters (detuning, power). Unexpectedly, we find that in a region of this parameter space the microwave resonance is irremediably destroyed: Only a dramatic power reset can restore the dynamics to its original state. The phenomenon can be understood as an optical instability linked to the Kerr nonlinearity of the cavity. A theory supporting this claim is presented, reproducing almost quantitatively the measurement. This remarkable feature might be further optimized and represents a new resource for quantum microwave circuits. Published by the American Physical Society 2024
Cavity optomechanics implements a unique platform where moving objects can be probed by quantum fields, either laser light or microwave signals. With a pump tone driving at a frequency above the cavity resonance, self-sustained oscillations can be triggered at large injected powers. These limit-cycle dynamics are particularly rich, presenting hysteretic behaviors, broad comb signals, and especially large motion amplitudes. All of these features can be exploited for both fundamental quantum research and engineering. Here we present low-temperature microwave experiments performed on a high- Q cavity resonance capacitively coupled to the flexure of a beam resonator. We study the limit-cycle dynamics parameter space as a function of pump parameters (detuning, power). Unexpectedly, we find that in a region of this parameter space the microwave resonance is irremediably destroyed: Only a dramatic power reset can restore the dynamics to its original state. The phenomenon can be understood as an optical instability linked to the Kerr nonlinearity of the cavity. A theory supporting this claim is presented, reproducing almost quantitatively the measurement. This remarkable feature might be further optimized and represents a new resource for quantum microwave circuits. Published by the American Physical Society 2024
Resonance-frequency fluctuations can limit the sensitivity and stability of superconducting microwave cavities used for qubit readout, optomechanical displacement sensing, and magnetic flux detection. Here, we demonstrate the suppression of resonance-frequency fluctuations by locking a noisy nonlinear superconducting microwave cavity to a strong pump tone. The Kerr nonlinearity of this system, whereby the resonance frequency depends on the intracavity field amplitude, gives rise to an intrinsic feedback mechanism that enables passive stabilization without active external feedback. Using two-tone spectroscopy, we experimentally characterize the intrinsic nonlinear feedback mechanism and investigate its temporal stability through Allan deviation analysis. The frequency fluctuations of the locked cavity mode are reduced by nearly two orders of magnitude, reaching the 1/f noise floor, without continuous frequency tracking or active control. Kerr locking provides a general approach for self-stabilizing nonlinear microwave resonators by suppressing low-frequency cavity noise while preserving sensitivity to signals outside the locking bandwidth. This approach may benefit a broad range of systems, including SQUID-based resonators, optomechanical devices, and parametric amplifiers.
A primary challenge in quantum science and technology is to isolate the fragile quantum states from their environment in order to prevent the irreversible leakage of energy and information which causes decoherence. In the late 1990s, however, a new paradigm emerged, in which the environment itself, as well as the coupling to this environment of the quantum state, are engineered in ways which, counterintuitively, facilitate the creation and stabilization of desired quantum properties. This paradigm, coined reservoir engineering, has been pursued experimentally in various implementations, in which the states of trapped ions, atomic clouds or artificial atoms based on superconducting circuits were driven into a desired target state using a dissipative reservoir. In all these cases, the cold electromagnetic environment served as the engineered reservoir, capitalizing on the tremendous progress in the ability to shape the modes of the electromagnetic field using masers and lasers. In optomechanics, which is the study of the coupling between light and mechanical motion, a similar scenario has been prevalent. Light is used to read out and control the mechanical motion, and in the past few years, various optomechanical architectures both in the optical and microwave domain have enabled to push mechanical systems into the quantum regime. These results can be interpreted in the context of reservoir engineering: cooling and many other optomechanical phenomena exploit the cold, dissipative nature of light. This thesis reports on the development of a multimode superconducting circuit with a mechanically compliant element - fitting into the field of circuit cavity electromechanics -, with which we pursue two themes. In the first set of experiments, reversing the roles of dissipation described above, we engineer the mechanical oscillator into a cold, dissipative environment for microwave light. The mechanical element is the fundamental mode of a free-standing top electrode of a capacitor, 100 nm thick and 32 micron in diameter made of aluminum with an effective mass of around 170 pg, vibrating at a resonance frequency of 5.5 MHz. The dissipative mechanical reservoir is prepared using an auxiliary microwave mode with engineered parameters.We utilize it to control the properties - in particular, the susceptibility - of the electromagnetic field and to perform low-noise amplification close to the quantum limit. The noise analysis reveals that the reservoir is close to its quantum ground state with a mean thermal occupation number well below 1, demonstrating its utility as a resource in the quantum regime. We also show that the system can be driven to the parametric instability threshold, above which self-sustained oscillations of the microwave field (masing) is observed. Finally, we demonstrate injection locking of the maser using an external seed pump. In a second set of experiments, a similar electromechanical circuit is used to implement a microwave isolator based on optomechanical interactions. The overarching theme is that dissipation of the mechanical oscillator, albeit intrinsic and not engineered via an auxiliary mode s a key ingredient for the device to function as a nonreciprocal frequency converter and isolator. In these experiments, an additional mechanical mode is used, such that a 4-mode optomechanical plaquette is realized.
High-gain and low-noise signal amplification is a valuable tool in various cryogenic microwave experiments. A microwave optomechanical device, in which a vibrating capacitor modulates the frequency of a microwave cavity, is one technique that is able to amplify microwave signals with high gain and large dynamical range. Such optomechanical amplifiers typically rely on strong backaction of microwave photons on the mechanical mode achieved in the sideband-resolved limit of optomechanics. Here, we observe microwave amplification in an optomechanical cavity in the extremely unresolved sideband limit. A large gain is observed for any detuning of the single pump tone within the cavity linewidth, a clear indication that the amplification is not induced by dynamical backaction. By being able to amplify for any detuning of the pump signal, the amplification center frequency can be tuned over the entire range of the broad cavity linewidth. Additionally, by providing microwave amplification without mechanical amplification, we predict that by using this scheme it is possible to achieve near-quantum-limited microwave amplification despite a large thermal occupation of the mechanical mode.
Superconducting optomechanical circuits enable frequency mixing of optical and mechanical modes, facilitating the generation of microwave frequency combs. However, such optomechanical combs suffer from frequency fluctuations, requiring their stabilization for applications in precision sensing and signal processing. Here, we investigate the sideband injection locking of microwave frequency combs in a niobium-based superconducting optomechanical circuit. By strongly driving the device with a blue-detuned pump to induce parametric instability and introducing an additional tone near individual comb peaks, we study how the locking range varies with the power, the frequency position, and the sweep direction of the injection tone. The locking responses show interesting features such as injection hysteresis, which cannot be explained by existing models. Numerical simulations of the classical optomechanical equations implementing a cubic mechanical nonlinearity show that the nonlinearity contributes to broadening the locking range. We also characterize the Allan deviations and phase noise of the injection-locked combs for different injection frequencies, demonstrating enhanced stability performance. Our results lay the foundation for the utilization of optomechanical combs for applications in nanomechanical sensing and cryogenic microwave pulse generation.
Nonlinearity is a key resource in both classical and quantum signal processing. Nonlinear nanomechanical elements have found applications ranging from sensing to computing, while networks of nonlinear resonators, as well as nonlinearly coupled networks of linear resonators, constitute promising platforms for simulating complex dynamics. Here, we experimentally demonstrate an approach to realizing strong mechanical nonlinearity in nanomechanical resonators, fully controlled through optical laser drives. The mechanism exploits the nonlinearity of the radiation-pressure interaction in a cavity optomechanical system, which gives rise to a nonlinear optical spring effect. The resulting Duffing nonlinearity is conveniently tunable in strength via pump laser power, while its sign is controlled by laser detuning. Moreover, we demonstrate that the nonlinear optical spring mediates effective interactions between mechanical modes coupled to a common cavity, inducing tunable nonlinear interactions between them that impact spectral response and dynamics. These results establish cavity optomechanics as a versatile and in-situ reconfigurable platform for engineering nonlinear dynamics in resonators and networks.
Squeezed light, displaying less fluctuation than vacuum in some observable, is key in the flourishing field of quantum technologies. Optical or microwave cavities containing a Kerr nonlinearity are known to potentially yield large levels of squeezing, which have been recently observed in optomechanics and nonlinear superconducting circuit platforms. Such Kerr-cavity squeezing however suffers from two fundamental drawbacks. First, optimal squeezing requires working close to turning points of a bistable cycle, which are highly unstable against noise thus rendering optimal squeezing inaccessible. Second, the light field has a macroscopic coherent component corresponding to the pump, making it less versatile than the so-called squeezed vacuum, characterised by a null mean field. Here we prove analytically and numerically that the bichromatic pumping of optomechanical and superconducting circuit cavities removes both limitations. This finding should boost the development of a new generation of robust vacuum squeezers in the microwave and optical domains with current technology.