Readout with strong drives beyond static or semi-classical approximations

There has been a remarkable push in recent years towards understanding the impact of strong drives in circuit quantum electrodynamics, especially in the context of readout. Several different tools have been developed to study this parameter regime. However, they broadly fall into two categories. The first involves characterizing the eigenspectrum and eigenstates of a static Hamiltonian, which in turn gives information about when to expect the drive to have a significant and often surprising impact on the dynamics. The second category essentially involves a semi-classical approximation in which one replaces the quantum resonator with a classical coherent tone, and the resulting time-dependent Hamiltonian is often studied using Floquet theory. Methods from both categories often provide qualitatively-similar predictions and  have been used to match experimental data to remarkable accuracy.

An open question remains however: does the quantum nature of the resonator ever impact the dynamics of strongly-driven systems?  In this work, we extend these tools to answer this question. We discuss in detail when the quantum-mechanical nature of the resonator is expected to modify the predictions of a static or semi-classical model. Focusing on readout, we further provide insight into when the simpler static or semi-classical models are valid.