Displaced circuit quantum electrodynamics beyond the critical photon number

Circuit quantum electrodynamics (cQED), exemplified by a coupled system of a superconducting qubit and a microwave cavity, is a powerful framework for quantum control and measurement of superconducting circuits. However, operations are typically restricted to low-photon-number regimes due to the strong nonlinearity introduced by Josephson junctions. In this work, we present a novel scheme for operating a cQED system with a large cavity field displacement, even in regimes far beyond the critical photon number. We find that a qubit drive at the bare cavity frequency can effectively displace the cavity field while minimizing the measurement-induced dephasing and the ac Stark shift. Furthermore, we demonstrate that standard cQED protocols—such as qubit control, readout, and cavity single-photon generation—remain compatible with these largely-displaced cavity fields. These findings open new pathways for exploring cQED dynamics in large-photon-number regimes, including the study of nonlinear phenomena in microwave cavities and the saturation of two-level system baths for microwave quantum states