We proposed an analytical model to analyze the Landau-Zener interference in a multilevel superconducting flux qubit driven by large-amplitude external fields. Our analytical results agree remarkably well with those of Berns et al. [Nature (London) 455, 51 (2008)]. Moreover, we studied the effect of driving frequency and dephasing rate on the interference. The dephasing generally destroys the interference, while increasing frequency rebuilds the interference at large dephasing rate. At a certain driving frequency and dephasing rate, the interference shows some anomalous features, as observed in recent experiments.
In this work we propose a way to unveil the type of environmental noise in strongly driven superconducting flux qubits through the analysis of the Landau-Zener-St\"uckelberg (LZS) interferometry. We study both the two-level and multilevel dynamics of the flux qubit driven by a
dc+ac magnetic field. We find that the LZS interference patterns exhibit well-defined multiphoton resonances whose shape strongly depends on the timescale and the type of coupling to a quantum bath. For the case of transverse system-bath coupling, the
n-photon resonances are narrow and nearly symmetric with respect to the dc magnetic field for almost all timescales, while in the case of longitudinal coupling they exhibit a change from a wide symmetric to an antisymmetric shape for times of the order of the relaxation time. We find this dynamic behavior relevant for the interpretation of several LZS interferometry experiments in which the stationary regime is not completely reached.