Dynamical semigroup Fokker–Planck equation approach to transient absorption and fluorescence upconversion spectroscopies

A dynamical semigroup Fokker–Planck equation, which meanwhile satisfies also the semiclassical detailed-balance relation at arbitrary temperatures, is constructed and further applied to nonlinear spectroscopic processes of two-surface molecular systems in condensed phases. Included in dissipation are the T1-vibrational relaxation and the pure T2-dephasing in both nuclear and electronic degrees of freedom. A mixed Heisenberg–Schrödinger picture of the field-dressed optical response function is proposed to efficient evaluation of pulsed-laser spectroscopies. Numerical simulations are carried out in a model one-dimensional dissipative Morse molecular system. Both the pump–probe absorption and the time-frequency resolved fluorescence spectra are demonstrated and analyzed in detail in terms of the underlying dissipative dynamics.