Beating experiment

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

In a standard beating experiment, a photomultiplier tube is used to detect the scattered light. Since the output photocurrent is proportional to the square of the electric field incident upon the tube, it is known as a square-law detector. Thus, if the scattered light contained only two frequencies, as would be the case if only two molecules were in the scattering volume (as in Figure 2), we find the magnitude of the photocurrent i to be... 

Dynamic Light Scattering. The measured single clipped photoelectron count autocorrelation function for the self-beating experiment has the form (5)... 

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... 

Ro-vibrational transitions in molecules provide an enormous number of narrow absorption lines in the infrared region. By using overtones of these transitions a large number of visible and near visible absorption lines could be provided. However, the weakness of these lines require very sensitive spectroscopic techniques. An example is the NICE OHMS technique [58, 67] where a gas sample of C2HD contained in a high finesse cavity absorbs at the (+ 3Vj) overtone at a 1064 nm. In beat experiments between this system and a iodine-stabilized YAG-laser, stabilities of below lO in 800 s have been observed. Especially interesting, is the demonstration of how this technique could be combined with the selective cold-atom technique to obtain line widths as narrow as 20 kHz. 

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,... 

Further discussion of polydisperse solutions is given in Section 8.10 in connection with light-beating experiments. 

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... 

Such a "self-beating experiment on biologically interesting molecules was first published by Dubin et al. (14), who made measurements of bovine serum albumin, ovalbumin, lysozyme, and polystyrene latex spheres. They also studied tobacco mosaic virus and DNA and found that the nonsphericity of these molecules leads to deviations from the Lenentzian spectrum. A theoretica] analysis by Pecoia (IS), which predicts angular-dependent, multi-Lorentzian spectra, can be used to obtain shape information of such molecules. 

Data on n(2)(Ax) and g(2)(x,AT) obtained in self-beating experiments can also be used to determine a set of average coherence times of the form... 

Experimentally, one finds that the hydrodynamic radius does scale like in 6 solvents, but in good solvents the situation is less clear. Dififri-sion or sedimentation experiments on polystyrene in toluene give D where the apparent exponent Vai is of order 0.53-0.54. More recent photon beat experiments give I aw = 0.55 0.02 for polystyrene in benzene. 

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

The following data of the self-beating experiment were obtained for a protein at 9 = 90°, T = 25°C, and concentration 40mg/mL ... 

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... 

Cleanliness of the sample cell is another issue that should not be overlooked. The sample cell should be clean and have minimum surface reflection otherwise the results may be greatly affected [22], Any dirt or scratch (e.g. a fingerprint) on the cell walls may behave like a local oscillator if it just happens to be illuminated by the incident beam. Thus, in a self-beating experiment (Scheme A, Figure 2.17), It will not be zero and the interpretation of the ACF using Eq. 2.34 will lead to unpredictable result. A useful check for the cleanliness of the medium and sample cell is to perform a quick PCS measurement of the medium only (better if made at a small scattering angle) this should produce a flat ACF with a very low count rate. 

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