Second-order Monte Carlo wave-function approach to the relaxation effects on ringing revivals in a molecular system interacting with a strongly squeezed coherent field

We investigate the relaxation effects on the quantum dynamics in a two-state molecular system interacting with a single-mode strongly amplitude-squeezed coherent field using the second-order Monte Carlo wave-function method. The molecular population inversion (collapse-revival behavior of Rabi oscillations) is known to show the echoes after each revival, which are referred to as ringing revivals, in the case of strongly squeezed coherent fields with oscillatory photon-number distributions due to the phase-space interference effect. Two types of relaxation effects, i.e., cavity relaxation (the dissipation of an internal single mode to outer mode) and molecular coherent (phase) relaxation caused by nuclear vibrations on ringing revivals are investigated from the viewpoint of the quantum-phase dynamics using the quasiprobability ( Q function) distribution of a single-mode field and the off-diagonal molecular density matrix ∣ρ_{elec  1,2}(t)∣ . It turns out that the molecular phase relaxation attenuates both the entire revival-collapse behavior and the increase in ∣ρ_{elec  1,2}(t)∣ during the quiescent region, whereas a very slight cavity relaxation particularly suppresses the echoes in ringing revivals more significantly than the first revival but hardly changes a primary variation in envelope of ∣ρ_{elec  1,2}(t)∣ in the nonrelaxation case.