Time-resolved spontaneous emission beyond the doorway-window approximation

A nonperturbative approach is developed for the calculation of time- and frequency-gated spontaneous emission spectra beyond the doorway-window approximation. The basic formulas are derived for the spectrum of a nonadiabatic system in a dissipative environment, which is excited by a pulse of arbitrary intensity and duration. This theory allows us to investigate transient effects due to the finiteness of (overlapping) excitation and gate pulses and to take into account the system-bath interaction during the pulses. To study the domain of validity of the doorway-window approach, the frequency integrated emission signal is calculated for a model electron-transfer system within the present general theory and compared with its doorway-window counterpart. The bath-induced dissipation is described in the framework of Redfield theory. The doorway-window approximation is found to perform quite well for pump durations which are shorter than vibrational periods, although quantitative differences exist. For pulses which are longer than vibrational periods, but shorter than periods of electronic coherences, the doorway-window approximation exaggerates the persistence of both electronic and vibrational coherences. For longer pulses, the doorway-window approach may even be qualitatively incorrect. Dissipative effects during the pump pulse are shown to manifest themselves through the quenching of vibrational coherences.