Modulation of gauge field for the parity-time phase transition in circuit QED

In this work, a parity-time (PT)-symmetric system is investigated based on superconducting circuits, which allows the tunability of atom-atom coupling using superconducting qubits. The calculation results demonstrate that the interaction between artificial atoms significantly impacts the transmission spectrum and the conditions of the phase transition in the system. When introducing a weak probe signal into the PT-symmetric system, several findings are observed. (1) The symmetry and intensity of both the linear and nonlinear outputs can be fine-tuned by adjusting the coupling strength between artificial atoms or manipulating the gauge-invariant phase in the system. (2) Nonreciprocal transmission can be achieved by driving different cavity modes. (3) The exceptional point (EP) of the PT phase transition can be adjusted within a certain range by modifying the gauge-invariant phase or adjusting the coupling strength in the system. One feasible experimental setup is also described and analyzed based on existing experimental techniques. These findings may inspire further research into modulating quantum phase transitions based on superconducting circuits.