Rotational quantum beats

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. 

As it turns out, in contradiction to the preceding considerations, rotational quantum beats have never been observed (to our knowledge). It also turns out that for large molecules there is a reasonable explanation for this fact. 

Now, the argument just presented relies on the unproven assumption that rotational quantum beats arising from a thermal sample of isolated molecules will wash each other out. Recently, we examined this assumption by directly simulating the decays associated with thermally averaged rotational beats.47 (Our initial motivation for this work was to try to explain the picosecond pump-probe results of Refs. 51 and 52, which results showed the existence of polarization-dependent early time transients in the decays of t-stilbene.) These theoretical simulations and subsequent picosecond-beam experiments47-50 have revealed that the manifestations of rotational coherence in thermally averaged decays can, in fact, be observed. In this section, we briefly review these results and examine some of their implications with regard to time-resolved studies of IVR. 

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. 

The effect of rotational constant mismatches on vibrational quantum beats43 is the subject of this subsection. We first review theoretical results that show that the qualitative effect of such mismatches is to increase the apparent damping rate of quantum beat envelopes relative to the decay rate of the unmodulated portion of a decay and that such beat damping rates increase with increasing rotational temperature. We then review results that show that such effects on beat damping are consistent with experiment. 

Zeeman quantum beat spectroscopy was used by Gouedard and Lehmann (1979, 1981) to measure the effect of various lu perturbing states on the gj-values [Eq. (6.5.21)] of more than 150 rotational levels of the Se2 B 0+ state (see Section 6.5.2 and Fig. 6.16). In that experiment, the excitation polarization was perpendicular to the applied magnetic field so that quantum beats were observed between nominal B-state components differing in M by 2. The frequencies of these beats increase linearly from 0 MHz at 0 G until the AM — 2 splitting falls... 

Stark quantum-beat (SQB) spectroscopy was used by Brieger, et al., (1980) for LiH A1E+ and by Schweda, et al., (1980, 1985) for BaO A1E+ to measure electric dipole moments of several rotation-vibration levels. In a A = 0 state, the electric-field-induced shift of a J, M-level is proportional to 2/B because jjStark hyg only A J -= 1, AM = 0 matrix elements ... 

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...

This suggests that a quantum beat spectrum of an AT-level system will, because it contains redundant information, be more complicated than the corresponding frequency domain spectrum. However, when the level spacings are approximately integer multiples of a common factor, such as 2B for upper-state A2F(J) = B (iJ + 2) rotational combination differences, then each upper state (J + 1, J — 1) pair of rotational levels coherently excited from all thermally populated lower-state J" levels contributes to a grand rephasing at tn = n [-gj ] (n = 1,2,...). This is Rotational Coherence Spectroscopy (RCS) (Felker and Zewail, 1987 and 1995 Felker, 1992). It provides upper state rotar tional constants without the need for a rotational analysis. 

In particular, the laboratory frame orientation of the transition moment for spontaneous fluorescence evolves in time. The intensities of z— and (x,y) — polarized fluorescence are modulated 7t/2 out of phase, but the intensity of the total x + y + z polarized fluorescence is not modulated. This is the physical basis for polarization quantum beats (Aleksandrov, 1964 Dodd, et al., 1964) and Rotational Coherence Spectroscopy (Felker and Zewail, 1995). 

In ref. [24] it has been proposed to measure quantum beats of the optical rotation in a special class of molecules with intermediate tunneling. This time dependence of the quantum beats gives experimental information about the parity violating coupling and indirectly also on the parity violating difference by reference to the tunneling splitting. 

N. OcM, H. Watanabe, S. Tsuchiya, S. Koda, Rotationally resolved laser-induced fluorescence and Zeeman quantum beat spectroscopy of the V B2 state of jet cooled CS2. Chem. Rhys. 113,271 (1987)... 

The rotational temperature of 10 K in the molecular beam leads to rotational quantum numbers in the range of 10 to 20. Using the rotational constants given by Ernst and Rakowsky [70], rotational periods are estimated to be several hundreds of picoseconds. Consequently, rotational recurrences, which might interfere with the observed vibrational beat structure, appear for the first time after more than 1 ns. Therefore, the influence of the rotational motion can be neglected in the simulation, as we concentrate on the dynamics up to a few picoseconds. 

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