Exact-WKB Analysis of Two-level Floquet Systems

Abstract

We explore the application of the exact Wentzel-Kramers-Brillouin (WKB) analysis to two-level Floquet systems and establish a systematic procedure to calculate the quasi-energy and Floquet effective Hamiltonian. We show that, in the exact-WKB analysis, the quasi-energy and Floquet effective Hamiltonian can be expressed in terms of cycle integrals (Voros symbol), which characterize monodromy matrices for Schr\"odinger-type differential equations governing two-level Floquet systems. We analytically evaluate the cycle integrals using the low-frequency expansion and derive both perturbative and non-perturbative corrections to the quasi-energy and Floquet effective Hamiltonian. To verify the accuracy of our results, we compare them with numerical calculations and analyze resonant oscillations, which reveal non-perturbative features that cannot be captured by the perturbative expansion.