Theory of Multi-photon Processes for Applications in Quantum Control

We present a general framework for evaluating multi-photon processes in periodically driven quantum systems, which are a versatile tool for engineering and controlling various quantum technology platforms. To achieve the accuracy required for such applications, the resulting effective coupling rates and frequency shifts, must be determined with very high precision. Here, we employ degenerate Floquet perturbation theory to evaluate the effective dynamics of driven quantum systems to arbitrary orders in the drive strength. As a specific example, we apply the framework 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theoretical predictions and exact numerical simulations, even in parameter regimes where previously known methods are no longer applicable.