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Floquet theory combined with the generalized Van Vleck nearly degenerateperturbation theory, has been widely employed for studying various two-levelsystems that are driven by external fields via the time-dependent longitudinal(i.e., diagonal) couplings. However, three-level systems strongly driven by thetime-dependent transverse (i.e., off-diagonal) couplings have rarely beeninvestigated, due to the breakdown of the traditional rotating waveapproximation. Meanwhile, the conventional perturbation theory is not directlyapplicable, since a small parameter for the perturbed part is no longerapparent. Here we develop a double-unitary-transformation approach to deal withthe periodically modulated and strongly driven systems, where thetime-dependent Hamiltonian has large off-diagonal elements. The first unitarytransformation converts the strong off-diagonal elements to the diagonal ones,and the second enables us to harness the generalized Van Vleck perturbationtheory to deal with the transformed Floquet matrix and also allows us to reducethe infinite-dimensional Floquet Hamiltonian to a finite effective one. For astrongly modulated three-level system, with the combination of the Floquettheory and the transformed generalized Van Vleck perturbation theory, we obtainanalytical results of the system, which agree well with exact numericalsolutions. This method offers a useful tool to analytically study themulti-level systems with strong transverse couplings.

An analytical double-unitary-transformation approach for strongly and periodically driven three-level systems