Tunable quantum interfaces between superconducting qubits and microwave photons induced by extreme driving

In this work, I investigate how to implement and quantify \emph{in-situ} tunable quantum interface between superconducting qubits and resonators using external transverse driving fields beyond the rotating wave approximation (RWA). When studying the system under the time-periodic driving field, we typically rely on RWA, a useful technique that significantly reduces the analytical difficulties in solving the dynamics with time-dependent Hamiltonian. Nonetheless, it does not correctly describe the systems' dynamics when the drive fields are excessively strong and far off-resonant. Especially in circuit QED platform, the RWA often breakdowns. Many studies before, however, mainly focus on the transition frequency shifts. How the RWA distorts the interaction rates between two systems has been rarely explored. I have performed quantitative studies over two different systems. One is the quantum Rabi model (QRM) where a two-level atom is dispersively coupled to a resonator mode. The other is dispersively coupled a transmon and resonator system, which is the same as the QRM except that the transmon replaces the two-level atom in QRM. In both cases, I have revealed that the RWA significantly mislead the sideband transition rates between two elements. In the latter case, I have performed the experiments, and the results nicely agree with the analytical and numerical calculations. In addition to these, I also have introduced a study where the tunable coupling between a transmon and resonator is used for non-invasive resonator probing.