Transmission properties and PT-symmetry in a hybrid quantum electromechanical system

We theoretically study the transmission properties and the PT-symmetry in a hybrid quantum electromechanical system consisting of a coplanar-waveguide (CPW) microwave cavity, a nanomechanical resonator (NAMR) and a superconducting transmon qubit, where the qubit works in the large detuning condition with both the CPW microwave cavity and the NAMR. By adjusting the NAMR-qubit coupling, we find that the transmissivity and the phase shift of the input field passing through the system can be tuned effectively. We also find that the effective electromechanical coupling can be greatly enhanced by adjusting the NAMR-qubit coupling. Furthermore, with the effective electromechanical coupling, we can realize the transition from the broken PT-symmetry phase to the unbroken PT-symmetry phase when both the cavity loss and the mechanical gain are considered. This work presents an effective way to manipulate the propagation characteristics and to study the PT-symmetry in a hybrid quantum electromechanical system.