The dissipative two-level system under strong ac-driving: a combination of Floquet and Van Vleck perturbation theory

TL;DR

This paper combines Floquet and Van Vleck perturbation theories to analyze the dissipative dynamics of a strongly driven two-level system, providing new analytical insights into relaxation, dephasing, and tunneling phenomena beyond traditional high-frequency approximations.

Contribution

It introduces a novel analytical approach that integrates Floquet and Van Vleck theories to accurately describe dissipative TLS dynamics under strong driving, extending beyond high-frequency limits.

Findings

Derived closed-form relaxation and dephasing rates.

Demonstrated suppression of tunneling at moderate frequencies.

Analyzed sensitivity of tunneling phenomena to external parameters.

Abstract

We study the dissipative dynamics of a two-level system (TLS) exposed to strong ac driving. By combing Floquet theory with Van Vleck perturbation theory in the TLS tunneling matrix element, we diagonalize the time-dependent Hamiltonian and provide corrections to the renormalized Rabi frequency of the TLS, which are valid for both a biased and unbiased TLS and go beyond the known high-frequency and rotating-wave results. In order to mimic environmental influences on the TLS, we couple the system weakly to a thermal bath and solve analytically the corresponding Floquet-Bloch-Redfield master equation. We give a closed expression for the relaxation and dephasing rates of the TLS and discuss their behavior under variation of the driving amplitude. Further, we examine the robustness of coherent destruction of tunneling (CDT) and driving-induced tunneling oscillations (DITO). We show that also for a moderate driving frequency an almost complete suppression of tunneling can be achieved for short times and demonstrate the sensitiveness of DITO to a change of the external parameters.