Theory of Multi-photon Processes for Applications in Quantum Control

We present a general theoretical framework for evaluating multi-photon processes in periodically driven quantum systems, which have been identified as a versatile tool for engineering and controlling nontrivial interactions in various quantum technology platforms. To achieve the accuracy required for such applications, the resulting effective coupling rates, as well as any drive-induced frequency shifts, must be determined with very high precision. Here, we employ degenerate Floquet perturbation theory together with a diagrammatic representation of multi-photon processes to develop a systematic and automatable approach for evaluating the effective dynamics of driven quantum systems to arbitrary orders in the drive strength. As a specific example, we demonstrate the effectiveness of this framework by applying it to the study of multi-photon Rabi oscillations in a superconducting fluxonium qubit, finding excellent agreement between our theoretical predictions and exact numerical simulations, even for large driving amplitude.