Coupling a mechanical oscillator to a parametric amplifier

In our experiment, we inductively couple a mechanical oscillator to a microwave circuit. We place a magnet on the tip of the mechanical resonator, a cantilever, which leads to a position dependent magnetic field. This field is coupled via a SQUID embedded into a microwave resonator: its resonance frequency depends on flux and consequently on the position of the cantilever. In addition to being a flux sensitive element, the SQUID also constitutes a non-linear element. This non-linear system is modelled with the Duffing model, describing our measurement data with good accuracy. The non-linearity also enables us to use the resonator as a parametric amplifier, and boost the system’s sensitivity.
By sideband cooling the cantilever – a macroscopic object – we aim to reach the quantum mechanical ground state. In the future we plan to replace the microwave resonator with a qubit, we can exploit strong single-photon single-phonon coupling for example by preparing the cantilever in a non-Gaussian state. In addition, our system can be used as a highly sensitive acceleration sensor.