Quantum beat-modulated fluorescence decay

Figure 2.26. Quantum beat-modulated fluorescence decay and its Fourier transform for the l W level of Sj thiophosgene. (Reprinted with permission from Ref. [42].)...

The situation changed, however, with two advances. The first advance was the discovery that in the S, - S0 spectrum of jet-cooled anthracene a second band exists (at S, + 1420 cm-1), the excitation of which gives rise to quantum beat-modulated fluorescence decays.40 Besides indicating a somewhat more global importance to the beat phenomenon in anthracene, the characteristics of these new beats provided very strong evidence that they arose as a manifestation of IVR. In particular, the beats were shown to have phases and modulation depths dependent on the fluorescence band detected. Such behavior, which... 

Figure 26. Quantum beat-modulated fluorescence decays observed for excitation of various bands (the excess S, vibrational energies are given in cm-1 in the figure) of jet-cooled c-stilbene. The particular fluorescence band detected for each decay is given by an asterisk in the appropriate spectrum in Fig. 24. All decays were obtained with 80 psec temporal resolution except the ones corresponding to the S, + 852 and 860 cm-1 excitations, which were measured with 300 psec resolution. R for the decays was 1.6 A, except the S, +821 and 987 cm 1 decays for which R = 3.2 and 16.0 A, respectively.

As previously discussed, if two or more excited eigenstates can combine in absorption with a common ground-state level, then these eigenstates can be excited so as to form a coherent superposition state. The superposition state, in turn, can give rise to quantum beat-modulated fluorescence decays. All this, of course, lies at the heart of the theory of vibrational coherence effects. However, it also implies that the same experimental conditions under which vibrational coherence effects are observed should allow for the observation of rotational coherence effects. That is, since more than one rotational level in the manifold of an excited vibronic state can combine in absorption with a single ground-state ro-vibrational level, then in a picosecond-resolved fluorescence experiment rotational quantum beats should obtain. 

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... 

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. 

The second major section (Section III), comprising the bulk of the chapter, pertains to the studies of IVR from this laboratory, studies utilizing either time- and frequency-resolved fluorescence or picosecond pump-probe methods. Specifically, the interest is to review (1) the theoretical picture of IVR as a quantum coherence effect that can be manifest in time-resolved fluorescence as quantum beat modulated decays, (2) the principal picosecond-beam experimental results on IVR and how they fit (or do not fit) the theoretical picture, (3) conclusions that emerge from the experimental results pertaining to the characteristics of IVR (e.g., time scales, coupling matrix elements, coupling selectivity), in a number of systems, and (4) experimental and theoretical work on the influence of molecular rotations in time-resolved studies of IVR. Finally, in Section IV we provide some concluding remarks. 

Other excitation energies Other than the ones at S, + 1380 and S, + 1420 cm-, there are three prominent bands in the intermediate region of jet-cooled anthracene s excitation spectrum. Time- and frequency-resolved measurements subsequent to excitation of these bands have also been made. Without going into any detail concerning the results of these measurements, we do note that all three excitations give rise to quantum beat-modulated decays whose beat patterns (phases and modulation depths) depend on the fluorescence band detected.42 Figure 16 shows an example of this behavior for excitation to S, + 1514 cm-1. The two decays in the figure correspond to the detection of two different fluorescence bands in the S, + 1514 cm-1 fluorescence spectrum. 

Fig. 23. The fluorescence decay of Cd vapor in a magnetic field, (a) Experimental data exhibiting the phenomenon of quantum beats, (b) The exponentially decaying component, (c) The decaying modulated component. This figure is reproduced from the work of Dodd, Kaul, and Warrington (158).

The detailed nature of the IVR in which the b -level participates is revealed by time-resolved results. One finds that the decays of individual bands in the 61 fluorescence spectrum are modulated by quantum beats, the phases and... 

The fluorescence rate is modulated at the frequency splitting of eigenstates +,M) and —, M ). This modulation is the quantum beat. The quantum beat decays at a rate... 

We have already discussed quantum-beat spectroscopy (QBS) in connection with beam-foil excitation (Fig.6.6). There the case of abrupt excitation upon passage through a foil was discussed. Here we will consider the much more well-defined case of a pulsed optical excitation. If two close-lying levels are populated simultaneously by a short laser pulse, the time-resolved fluorescence intensity will decay exponentially with a superimposed modulation, as illustrated in Fig. 6.6. The modulation, or the quantum beat phenomenon, is due to interference between the transition amplitudes from these coherently excited states. Consider the simultaneous excitation, by a laser pulse, of two eigenstates, 1 and 2, from a common initial state i. In order to achieve coherent excitation of both states by a pulse of duration At, the Fourier-limited spectral bandwidth Au 1/At must be larger than the frequency separation ( - 2)/ = the pulsed excitation occurs at... 

If two or more closely spaced molecular levels are simultaneously excited by a short laser pulse, the time-resolved total fluorescence intensity emitted from these coherently prepared levels shows a modulated exponential decay. The modulation pattern, known as quantwn beats is due to interference between the fluorescence amplitudes emitted from these coherently excited levels. Although a more thorough discussion of quantum beats demands the theoretical framework of quantum electrodynamics [11.33], it is possible to understand the basic principle by using more simple argumentation. 

Fig.11.23a,b. Quantum beat spectroscopy, (a) Level scheme illustrating coherent excitation of levels 1 and 2 with a short broad-band pulse, (b) Fluorescence intensity showing a modulation of the exponential decay... 

---