Vibrational quantum beats phases

Figure 9.5 The phase of a vibrational quantum beat depends on whether the bright state for the excitation step is bright or dark in the fluorescence detection step, A molecular beam of anthracene, rotationally cooled to 3K, is excited by a 15 picosecond pulse at 1420 cm-1 above the Si <— So 0q origin band. Fluorescence is detected in a selected wavelength region through...

The events taking place in the RCs within the timescale of ps and sub-ps ranges usually involve vibrational relaxation, internal conversion, and photo-induced electron and energy transfers. It is important to note that in order to observe such ultrafast processes, ultrashort pulse laser spectroscopic techniques are often employed. In such cases, from the uncertainty principle AEAt Ti/2, one can see that a number of states can be coherently (or simultaneously) excited. In this case, the observed time-resolved spectra contain the information of the dynamics of both populations and coherences (or phases) of the system. Due to the dynamical contribution of coherences, the quantum beat is often observed in the fs time-resolved experiments. 

Fig. 6.5. Numerical simulation of quantum beats measurements of DLL mutant RCs of Rb. capsulatus with 80 fsec pump pulse. Two vibrational frequencies are included in the simulation. The box with broken line indicates the time region in which the phase evolution of the vibrational quantum beams can be seen clearly.

Subsequent to the anthracene studies, picosecond-beam measurements of IVR in a number of other molecules have been made. These molecules include deuterated anthracenes,44 t-stilbene,45 and some alkyl anilines.46 One of the most significant results of these studies is that they have indicated that vibrational coherence30,40 (phase-shifted quantum beats) is a general phenomenon in molecules. Thus, it appears that an accurate understanding of IVR must rest firmly on an accurate understanding of vibrational coherence. 

The observation of novel quantum beats in the spectrally resolved fluorescence of anthracene21 forced one to consider, within the context of radiationless transition theory, the details of how IVR might be manifested in beat-modulated fluorescence decays. This work led to the concepts of phase-shifted quantum beats and restricted IVR,30a,4° and to a general set of results306 pertaining to the decays of spectrally resolved fluorescence in situations where an arbitrary number of vibrational levels, coupled by anharmonic coupling, participate in IVR. Moreover, three regimes of IVR have been identified no IVR, restricted (or coherent) IVR, and dissipative IVR.42... 

The short-time spike in the decay, which can be attributed to the dephasing of many quantum beat terms (all with + 1 phases), represents the irreversible flow of vibrational energy out of the zero-order state prepared by the laser. The long-time component, although weakly modulated, represents an equilibration in the distribution of vibrational energy subsequent to the initial energy flow process. 

A theory for the ultrafast pump-probe spectroscopy of large polyatomic molecules in condensed phases was developed in the work [15]. A multimode Brownian oscillator model was used to account for high-frequency molecular vibrations and local intermolecular modes as well as collective solvent motions. A semiclassical picture was provided using the density matrix in Liouville space. Conditions for the observation of quantum beats, spectral diffusion, and solvation dynamics (dynamic Stokes shift) are specified. 

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