Semiclassical many-mode Floquet theory. IV. Coherent population trapping and SU(3) dynamical evolution of dissipative three-level systems in intense bichromatic fields

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Abstract
The many-mode Floquet theory (MMFT) recently developed by authors is extended to incorporate the irreversible damping mechanisms for the nonperturbative treatment of the dynamical evolution of dissipative three-level systems at two-photon or multiphoton coherent resonance trapping conditions induced by two strong linearly polarized monochromatic fields. It has been recently shown by several workers that under the rotating-wave approximation (RWA), population may be permanently trapped in the three-level system if the coherent monochromatic fields are exactly two-photon resonant with the initial and final states, decoupled from the intermediate decaying level. In practice, the inclusion of the non-RWA terms necessarily modifies the resonant trapping conditions and behavior. In this paper we extend the generalized Van Vleck (GVV) nearly degenerate perturbation theory to an analytical treatment of the non-Hermitian two-mode Floquet Hamiltonian. This reduces the infinite-dimensional time-independent non-Hermitian Floquet Hamiltonian to a 3×3 effective Hamiltonian, from which essential properties of the coherent population-trapping behavior as well as the dynamical evolution of the dissipative SU(3) coherence vector S→(t) can be readily obtained and expressed in terms of only three complex quasienergy eigenvalues and eigenvectors. The MMFT-GVV studies show that the RWA two-photon resonant trapping condition is substantially modified by the effects of non-RWA terms, and that the system can be ‘‘quasitrapped’’ for only a finite amount of time characterized by a small imaginary energy (width) associated with a coherent superposition state of the initial and final levels. Furthermore, it is found that the initially eight-dimensional coherence vector S→(t) evolves predominantly to a one-dimensional scalar at the two-photon or multiphoton resonant quasitrapping conditions. Detailed results and pictorial representations of the population trapping and SU(3) dissipative dynamical evolution are presented.