Parametrically enhanced interactions and non-trivial bath dynamics in a photon-pressure Kerr amplifier

Photon-pressure coupling between two superconducting circuits is a promising platform for investigating radiation-pressure coupling in novel parameter regimes and for the development of radio-frequency (RF) quantum photonics and quantum-limited RF sensing. So far, the intrinsic Josephson nonlinearity of photon-pressure coupled circuits has not been considered a potential resource for enhanced devices or novel experimental schemes. Here, we implement photon-pressure coupling between a RF circuit and a microwave cavity containing a superconducting quantum interference device (SQUID) which can be operated as a Josephson parametric amplifier (JPA). We demonstrate a Kerr-based enhancement of the photon-pressure single-photon coupling rate and an increase of the cooperativity by one order of magnitude in the amplifier regime. In addition, we characterize the upconverted and Kerr-amplified residual thermal fluctuations of the RF circuit, and observe that the intracavity amplification reduces the measurement imprecision. Finally, we demonstrate that RF mode sideband-cooling is surprisingly not limited to the effective amplifier mode temperature arising from quantum noise amplification, which we explain by non-trivial bath dynamics due to a two-stage amplification process. Our results demonstrate how Kerr nonlinearities and in particular Josephson parametric amplification can be utilized as resource for enhanced photon-pressure systems and Kerr cavity optomechanics.