Floquet dynamics of Rabi model beyond the counterrotating hybridized rotating wave method

TL;DR

This paper develops a comprehensive analytical approach to the Floquet dynamics of the Rabi model, extending understanding beyond previous methods and enabling better quantum control in strong driving regimes.

Contribution

It introduces a combined analytical method that covers nearly all parameter regimes of the Rabi model, clarifies the physics of its dynamics, and explores dissipative effects under strong driving.

Findings

Analytical results agree well with numerical and experimental data.

Dynamic frequencies shift from Rabi frequency to multiples of driving frequency as intensity increases.

Dissipation effects are tunable and match numerical predictions in strong driving regimes.

Abstract

Monochromatically driven two-level systems (i.e., Rabi models) are ubiquitous in various fields of physics. Though they have been exactly solved, the physical pictures in these exact solutions are not clear. Recently, approximate analytical solutions with neat physics have been obtained by using the counterrotating hybridized rotating wave (CHRW) method, which has been proven to be effective over a wider range of parameters than the previous analytical solutions. However, the CHRW depends on a parameter {\xi}, which has no solution in some regimes. Here we combine the double-unitary-transformation approach with the generalized Van Vleck nearly degenerate perturbation theory, and present approximate analytical results with clear physics for almost all parameter regimes, which agree well with the numerical solutions and the previous experimental results. Moreover, the dynamic frequencies of the Rabi model are regular, and the frequency with the highest Fourier amplitude changes from the Rabi frequency to 2n{\omega} with driving frequency {\omega} and integer n, as the driving intensity increases from weak to deep-strong. In addition, we further explore the Floquet dynamics of the dissipative open Rabi model. Remarkably, the dissipations are tunable in the rotating frame, and the approximate analytical results obtained by our method are in good agreement with the numerical results in the strong driving regime. These results pave the way to quantum control using strong and deep-strong driving with applications in quantum technologies.