Floquet-Liouville supermatrix approach: Time development of density-matrix operator and multiphoton resonance fluorescence spectra in intense laser fields

A Floquet-Liouville supermatrix {FLSM) approach is presented for nonperturbative treatment of the time development of the density-matrix operator of atoms and molecules exposed to intense polychromatic fields. By extending the many-mode Floquet theory (MMFT) recently developed, the time-dependent Liouville equation for the density matrix of quantum systems undergoing relaxations (due to radiative decays and collisional dampings, etc. ) can be transformed into an equivalent time-independent non-Hermitian FLSM eigenvalue problem. This yields a numerically stable and computationally efficient approach for the unified treatment of nonresonant and resonant, one- and multiple-photon, steady-state and transient phenomena in nonlinear optical processes, much beyond the conventional rotating-wave-approximation (RWA) method. Connections of the FLSM approach to the MMFT in the limit of zero relaxations are also made, providing the understanding of the physical significance of FLSM supereigenvalues and eigenvectors. In addition to the exact FLSM formalism, we have also presented higher-order perturbative results, based on the extension of the generalized Van Vleck {GVV) nearly degenerate perturbation theory, appropriate for somewhat weaker fields and near-resonant processes, but beyond the R%A limit. The implementation of the GVV method in the time-independent Floquet-Liouvillian allows the reduction of the infinitedimensional FLSM into a finite-dimensional GVV-Liouville matrix, from which essential analytical results are readily obtained. As an illustration of the usefulness of the new formalism, we extend both the FLSM and the GVV methods to a formal study of the multiphoton-induced resonance fluorescence spectra of two-level systems subject to purely radiation relaxations. Both the timeaveraged power spectrum and the time-dependent physical spectrum are exploited in details, and novel new features in intense fields are pointed out. I. INTRODUCTION The investigation of nonlinear optical processes induced by intense laser fields such as multiphoton ionization and dissociation of atoms and molecules, resonance fiuorescence, Raman scatterings, and wave mixings, etc. , is a topic of much current interest' both theoretically and experimentally. At lower fields, perturbative and diagrammatic methods are often used for nonresonant phenomena, whereas the rotating-wave approximation (RWA) is most commonly adopted for near-resonant processes. The semiclassical Floquet approaches based on the Schrodinger equation, while providing nonperturbative techniques for the studies of multiphoton ionization, excitation, and dissociation processes at high fields, cannot be applied to processes undergoing relaxations due to radiative decays and collision dmnpings, etc. In this paper we present a general nonperturbative semiclassical treatment of the Liouville equation (allowing for relaxation mechanisms} for the density-matrix operator of atomic or molecular systems exposed to intense monochromatic or polychromatic fields. By extending the many-mode Floquet theory (MMi l') recently developed, the timedependent Liouville equation can be transformed into an