Quantum beat experiment

Turning now to the quantum beat experiment, we find that the differential counting rate is given by... 

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... 

Although a simple Fourier transform relationship can exist between a high spectral resolution frequency domain experiment and a time-domain quantum beat experiment, whenever the excitation and detection steps involve electromagnetic radiation of different spectral, spatial, or temporal characteristics, the intrinsic information content of time and frequency domain experiments needs not be identical. The format in which the information is presented may be more transparently interpretable in either the time or frequency domain. 

The earliest pulsed laser quantum beat experiments were performed with nanosecond pulses (Haroche, et al., 1973 Wallenstein, et al., 1974 see review by Hack and Huber, 1991). Since the coherence width of a temporally smooth Gaussian 5 ns pulse is only 0.003 cm-1, (121/s <-> 121 cm"1 for a Gaussian pulse) nanosecond quantum beat experiments could only be used to measure very small level splittings [e.g. Stark (Vaccaro, et al., 1989) and Zeeman effects (Dupre, et al., 1991), hyperfine, and extremely weak perturbations between accidentally near degenerate levels (Abramson, et al., 1982 Wallenstein, et al., 1974)]. The advent of sub-picosecond lasers has expanded profoundly the scope of quantum beat spectroscopy. In fact, most pump/probe wavepacket dynamics experiments are actually quantum beat experiments cloaked in a different, more pictorial, interpretive framework,... 

In most quantum beats experiments, the radical pairs were generated whose ESR spectra were either known or could be obtained independently, e.g., using the OD ESR method. These experiments [23,24] show a fair agreement between the observed beat frequencies and the splittings in the ESR spectra of a pair. Figure 7 shows the recent results of the study of quantum beats in the systems... 

We will return to quantum-beat experiments in Sect.9.4.6, where the more well-defined case of optical (laser) excitation is discussed. 

In a Zeeman quantum-beat experiment of the 4p 5s 82 state in the selenium atom the excitation was performed at 207 nm from the groimd state P2 using linearly polarised light from a pulsed laser. In the decay a signal curve in an external magnetic field as illustrated below was obtained. 

The time resolved fluorescence intensity measured in a quantum beat experiment, can be represented by... 

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. 

Recently, Scherer et al. have used the 10-fs laser pulse with A,excitation = 860 nm to study the dynamical behavior of Rb. Sphaeroides R26 at room temperatures. In this case, due to the use of the 10-fs pulse both P band and B band are coherently excited. Thus the quantum beat behaviors are much more complicated. We have used the data given in Table I and Fig. 19 to simulate the quantum beat behaviors (see also Fig. 22). Without including the electronic coherence, the agreement between experiment and theory can not be accomplished. 

Magnetic quantum beats in the transient process after pulsed depopulation of the ground state may be observed not only in fluorescence, but also in a more direct way, namely in absorption. In connection with what was discussed in Section 3.5, one must expect maximum sensitivity if the experiment is conducted according to the laser interrogated dichroism method see Fig. 3.17. To this end it is convenient to direct the external magnetic field B along the 2-axis as shown in Fig. 4.21 where the probe beam E-vector can be either in the xy plane (Em) or in the yz plane (Epr2). 

Quantum beats have been observed in a variety of experiments, particularly in beam—foil measurements. Teubner et al. (1981) were the first to observe quantum beats in electron—photon coincidence measurements, using sodium as a target. The zero-field quantum beats observed by them are due to the hyperfine structure associated with the 3 Pii2 excited state (see fig. 2.20). The coincidence decay curve showed a beat pattern... 

At this point, it may seem to the reader that the detailed consideration of quantum beat phase distributions is a somewhat abstract exercise bearing little relation to IVR. We would justify our attention to the problem of phases by noting that the proper interpretation of experimental results from picosecond-jet experiments on IVR relies on the ability to determine how closely one s experimental conditions correspond to one s theoretical model of the experiment. A particularly convenient way to do this is by comparing phase characteristics from experiment with those from theory. In addition, phase characteristics are useful in helping one assign the various bands in a fluorescence spectrum to band types. 

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. 

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. 

Anticrossing, Quantum-Beat, and Double-Resonance Experiments... 

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... 

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