New exact results for periodically driven two-level and spin systems

Analytical calculations of infinite summations involving Bessel functions are employed to investigate various results in Floquet physics that were previously only partially known numerically. Our analysis includes evaluating the transition rates in the Landau-Zener-Stückelberg-Majorana interferometry of superconducting qubits, which results in several novel asymptotic expressions for the rate and related quantities. We also present analogous findings for the fluorescence spectrum of quantum dot systems. A further illustration pertains to the periodic driving of quantum spin systems. Specifically, we undertake an analytical characterization of the effective interactions of a Hubbard model subjected to a varying time-periodic electric field. This enables us to determine the reversal of signs in the effective interactions, one of the hallmarks in the reversible tuning of magnetic interactions in Mott insulators, via Bessel zeros.