Flux-mediated electromechanical coupling between a mechanical oscillator and superconducting qubit

Control over the quantum states of a massive oscillator is important for several technological applications and to test the fundamental limits of quantum mechanics. In recent years, hybrid devices consisting of superconducting qubit and mechanical resonator have emerged as a successful candidate in this regard. Here we explore the performance of a hybrid electromechanical system based on the magnetic flux-based coupling. The coupling stems from the quantum interference of the superconducting phase across the tunnel junction and is realized by embedding a mechanical resonator in a superconducting loop. Our results show that the single-photon coupling rates higher than the conventional optomechanical systems in the microwave domain can be reached by this approach. With this large coupling rate, we detect the thermo-mechanical motion by driving the system with less than one photon and observe the Landau-Zener-Stückelberg effect.