Landau-Zener-St\"uckelberg spectroscopy of a fluxonium quantum circuit

In this work, we study the time-averaged populations obtained for a fluxonium circuit under a large amplitude nonresonant periodic drive. We present numerical simulations of the time evolution which consider the multi-level structure of the driven quantum circuit, looking for a realistic modeling closer to experimental implementations. The Landau-Zener-St\"uckelberg spectra show resonances that can be understood as originated from constructive interference favoring transitions to higher levels. For a truncated two-level system (TLS) the resonance patterns can be interpreted using a simplified description of the avoided crossing that takes into account the dynamic phase accumulated at each operation point. For the multilevel case, we derive an effective two-level Hamiltonian using a Schrieffer-Wolff transformation starting from the Floquet Hamiltonian in the Sambe space. Our study provides predictive insight into experimental outcomes, offering an intuitive interpretation that could also support the implementation of fast-non-adiabatic single-qubit gates and entangling protocols.