PT symmetry in a superconducting hybrid quantum system with longitudinal coupling

We propose a scheme consisting of coupled nanomechanical cantilever resonators and superconducting flux qubits to engineer a parity-time- (PT-) symmetric phononic system formed by active and passive modes. The effective gain (loss) of the phonon mode is achieved by the longitudinal coupling of the resonator and the fast dissipative superconducting qubit with a blue-sideband driving (red-sideband driving). A PT-symmetric to broken-PT-symmetric phase transition can be observed in both balanced gain-to-loss and unbalanced gain-to-loss cases. Applying a resonant weak probe field to the dissipative resonator, we find that (i) for balanced gain and loss, the acoustic signal absorption to amplification can be tuned by changing the coupling strength between resonators; (ii) for unbalanced gain and loss, both acoustically induced transparency and anomalous dispersion can be observed around Delta = 0, where the maximum group delay is also located at this point. Our work provides an experimentally feasible scheme to design PT-symmetric phononic systems and a powerful platform for controllable acoustic signal transmission in a hybrid quantum system.

Automated summary

We propose a scheme using coupled nanomechanical cantilever resonators and superconducting flux qubits to create a parity-time-(PT-)symmetric phononic system with active and passive modes. By coupling the resonator and fast dissipative superconducting qubit longitudinally and using blue-sideband driving (red-sideband driving), we achieve effective gain (loss) for the phonon mode. A transition from PT-symmetric to broken-PT-symmetric phase can be observed for both balanced and unbalanced gain-to-loss cases. Our work presents an experimentally feasible method for designing PT-symmetric phononic systems and enables controllable acoustic signal transmission in a hybrid quantum system.