Floquet formulation for the investigation of multiphoton quantum interference in a superconducting qubit driven by a strong ac field

Abstract

We present a Floquet treatment of multiphoton quantum interference in a strongly driven superconducting flux qubit. The periodically time-dependent Schr\"odinger equation can be reduced to an equivalent time-independent infinite-dimensional Floquet matrix eigenvalue problem. For resonant or nearly resonant multiphoton transitions, we extend the generalized Van Vleck (GVV) nearly degenerate high-order perturbation theory for the treatment of the Floquet Hamiltonian, allowing the reduction of the infinite-dimensional Floquet matrix to an $N\ifmmode\times\else\texttimes\fi{}N$ effective Hamiltonian, where $N$ is the number of eigenstates under consideration. The GVV approach allows accurate treatment of ac Stark shift, power broadening, time-dependent and time-averaged transition probability, etc., well beyond the rotating wave approximation. We extend the Floquet and GVV approaches for numerical and analytical studies of the multiphoton resonance processes and quantum interference phenomena for the superconducting flux qubit system $(N=2)$ driven by intense ac fields.