Vibrational quantum beats

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...

In conventional theories of rate processes, the temperature T is usually involved. The involvement of T implicitly assumes that vibrational relaxation is much faster than the process under consideration so that vibrational equilibrium is established before the system undergoes the rate process. For example, let us consider the photoinduced ET (see Fig. 5). From Fig. 5 we can see that for the case in which vibrational relaxation is much faster than the ET, vibrational equilibrium is established before the rate process takes place in this case the ET rate is independent of the excitation wavelength and a thermal average ET constant can be used. On the other hand, for the case in which the ET is much faster than vibrational relaxation, the ET takes place from the pumped vibronic level (or levels) and thus the ET rate depends on the excitation wavelength and often quantum beat will be observed. 

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. 

By using transient absorption spectroscopic techniques, time-resolved measurements of photo-induced interfacial ET with time-constants shorter than 100 fsec have become possible [51,52,58-60]. When ultrashort laser pulses are used in studying PIET, vibrational coherences (or vibrational wave packet) can often be observed and have indeed been observed in a number of dye-sensitized solar cell systems. This type of quantum beat has also been observed in ultrafast PIET in photosynthetic reaction center [22], It should be noted that when the PIET takes place in the time scale shorter than 100 fsec, vibrational relaxation between the system and the heat bath is slower than PIET this is the so-called vibrationally non-relaxed ET case, and it will be treated in this section. 

Figure 5.4, one can easily understand why the interfacial electron transfer should take place in the 10-100 fsec range because this ET process should be faster than the photo-luminescence of the dye molecules and energy transfer between the molecules. Recently Zimmermann et al. [58] have employed the 20 fsec laser pulses to study the ET dynamics in the DTB-Pe/TiC>2 system and for comparison, they have also studied the excited-state dynamics of free perylene in toluene solution. Limited by the 20 fsec pulse-duration, from the uncertainty principle, they can only observe the vibrational coherences (i.e., vibrational wave packets) of low-frequency modes (see Figure 5.5). Six significant modes, 275, 360, 420, 460, 500 and 625 cm-1, have been resolved from the Fourier transform spectra of ultrashort pulse measurements. The Fourier transform spectrum has also been compared with the Raman spectrum. A good agreement can be seen (Figure 5.5). For detail of the analysis of the quantum beat, refer to Figures 5.5-5.7 of Zimmermann et al. s paper [58], These modes should play an important role not only in ET dynamics or excited-state dynamics, but also in absorption spectra. Therefore, the steady state absorption spectra of DTB-Pe, both in...

For comparison, the same calculation, except changing the vibrational frequency to 275 cm-1, is shown in Figure 5.12. The feature of the dynamics is mostly similar, except that the period of the quantum beat is longer. Therefore, hereafter the focus shall only be put on the results for 420 cm-1 mode. 

Let us start with the quantum beats measurements of DLl mutant RCs of Rb. capsulatns with 80 fsec pump pulse, which was reported by Matrin et al. [75,76]. This mutant lacks bacterial pheophetines so that ET does not take place in the picosecond time scale. In other words, the quantum beats result from a coherent excitation of vibrational states. In the observed... 

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.

Martin s group has also performed the same type of measurements to wild-type RCs of Rh. sphaeroides [77], A rapid ET takes place upon an excitation of the special pair in this system. Since the bandwidth of the pumping pulse can only cover one electronic state (special pair), quantum beats result from a generation of the vibrational coherence. However, the system also exhibits single-vibronic ET. In this case, the coupled-master equations can be written as... 

Fourth, the Si —> S0 fluorescence exhibits loss of emission at low Si excess vibrational energy and reappearance at very large excess energies, consistent with predissociation. A quantum beat-modulated Si fluorescence decay was observed at energies corresponding to the expected position of the T2 (71,71 ) state. 

It should be noted that the laser pump pulses create sets of intermolecular rovibrational coherence. For example, quantum beats appear in time profile of the CARS spectrum from a molecular mixture. - The beat frequency created is equal to the difference between frequencies of vibrational modes of molecules in the mixture. When many sets of inteimolecular... 

The time-dependent oscillations in absorption or other observables can be thought of as quantum beats resulting from coherent excitation of several vibronic levels contained within the bandwidth of the ultrashort excitation pulse. In a formal sense, the experiment is the same as other quantum beat experiments carried out on femtosecond or longer time scales. However, in most such experiments different molecular vibrational degrees of freedom that... 

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... 

---