Nonlinear Josephson circuits play a crucial role in the growing landscape of quantum information and technologies. The typical circuits studied in this field consist of qubits, whoseanharmonicity is much larger than their linewidth, and also of parametric amplifiers, which are engineered with linewidths of tens of MHz or more. The regime of small anharmonicity but also narrow linewidth, corresponding to the dynamics of a high-Q Duffing oscillator, has not been extensively explored using Josephson cavities. Here, we use two-tone spectroscopy to study the susceptibility of a strongly driven high-Q Josephson microwave cavity. Under blue-detuned driving, we observe a shift of the cavity susceptibility, analogous to the AC Stark effect in atomic physics. When applying a strong red-detuned drive, we observe the appearance of an additional idler mode above the bifurcation threshold with net external gain. Strong driving of the circuit leads to the appearance of two exceptional points and a level attraction between the quasi-modes of the driven cavity. Our results provide insights on the physics of driven nonlinear Josephson resonators and form a starting point for exploring topological physics in strongly-driven Kerr oscillators.
The nonlinear, parametric coupling between two harmonic oscillators has been used in the field of optomechanics for breakthrough experiments regarding the control and detection of mechanicalresonators. Although this type of interaction is an extremely versatile resource and not limited to coupling light fields to mechanical resonators, there have only been, very few reports of implementing it within other systems so far. Here, we present a device consisting of two superconducting LC circuits, parametrically coupled to each other by a magnetic flux-tunable photon-pressure interaction. We observe dynamical backaction between the two circuits, photon-pressure-induced transparency and absorption, and enter the parametric strong-coupling regime, enabling switchable and controllable coherent state transfer between the two modes. As result of the parametric interaction, we are also able to amplify and observe thermal current fluctuations in a radio-frequency LC circuit close to its quantum ground-state. Due to the high design flexibility and precision of superconducting circuits and the large single-photon coupling rate, our approach will enable new ways to control and detect radio-frequency photons and allow for experiments in parameter regimes not accessible to other platforms with photon-pressure interaction.
In recent years, the field of microwave optomechanics has emerged as leading platform for achieving quantum control of macroscopic mechanical objects. Implementations of microwave optomechanicsto date have coupled microwave photons to mechanical resonators using a moving capacitance. While simple and effective, the capacitive scheme suffers from inherent and practical limitations on the maximum achievable coupling strength. Here, we experimentally implement a fundamentally different approach: flux-mediated optomechanical coupling. In this scheme, mechanical displacements modulate the flux in a superconducting quantum interference device (SQUID) that forms the inductor of a microwave resonant circuit. We demonstrate that this flux-mediated coupling can be tuned in-situ by the magnetic flux in the SQUID, enabling nanosecond flux tuning of the optomechanical coupling. Tuning the external in-plane magnetic transduction field, we observe a linear scaling of the single-photon coupling strength, reaching rates comparable to the current state-of-the-art. Finally, this linear scaling is predicted to overcome the limits of single-photon coupling rates in capacitive optomechanics, opening the door for a new generation of groundbreaking optomechanical experiments in the single-photon strong coupling regime.