Pump-Probe Time-Resolved Stimulated Emission Spectra

Ultrafast radiationless transitions are often observed through ultrashort pump-probe time-resolved measurements. In this section, a theoretical formula of the pump-probe time-resolved stimulated emission spectra is briefly introduced and the relationship between the dynamics calculation and the pump-probe spectra are presented. For this purpose, the dynamics of a simple model system with vibrationally non-equilibrated is discussed. For a real application of the theoretical treatment given in this chapter, ultrafast charge transfer taking place in photosynthetic RCs is studied. 

Pump-Probe Time-Resolved Stimulated Emission Spectra 

Here a model for the pump-probe time-resolved measurement of a system with two vibronic manifolds and m embedded in a heat bath is considered. The two vibronic manifolds are coupled by the interaction H.  

A pumping laser excites the system from the ground vibronic manifold g to the excited vibronic manifold n. After excitation, a probing laser is applied to induce transitions from the manifold to the manifold g via stimulated emission and/or to higher excited manifolds via induced absorption. This work shall focus on the pump-probe time-resolved stimulated emission experiment. In this case, an expression for the time-resolved profiles is derived in terms of the imaginary part of the transient susceptibility X (copu,copr, x). In the adiabatic approximation and the Condon approximation, it has been shown that [18,21] 

Here mpu, mpr, t, and Jlnf) represent the central frequency of the pumping laser, that of the probing laser, the time interval between the two pulses, and the transition dipole moment, respectively and Fnri(copr) is the band-shape function associated with the probing optical process. In Eq. (128), plm, is the density matrix element of the molecular system after excitation by the pump pulse. 

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Pump-Probe Time-Resolved Stimulated Emission Spectra. 204... 

Describing complex wave-packet motion on the two coupled potential energy surfaces, this quantity is also of interest since it can be monitored in femtosecond pump-probe experiments [163]. In fact, it has been shown in Ref. 126 employing again the quasi-classical approximation (104) that the time-and frequency-resolved stimulated emission spectrum is nicely reproduced by the PO calculation. Hence vibronic POs may provide a clear and physically appealing interpretation of femtosecond experiments reflecting coherent electron transfer. We note that POs have also been used in semiclassical trace formulas to calculate spectral response functions [3]. 

Being mainly interested in the dynamics associated with the conical intersection of the and S2 excited electronic states, we focus in the following on the excited-state contribution to the pump-probe spectrum. Figures 2 and 3 compare three different excited-state pump-probe signals, namely the integral stimulated-emission spectrum (2b), the time-resolved fluorescence spectrum (3a), and the dispersed stimulated-emission spectrum (3b). As has been discussed above, the integral stimulated-emission spectrum and the time-resolved fluorescence spectrum are rather similar. Because of the... 

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