Hyperfine quantum beats

When, however, phonons of appropriate energy are available, transitions between the various electronic states are induced (spin-lattice relaxation). If the relaxation rate is of the same order of magnitude as the magnetic hyperfine frequency, dephasing of the original coherently forward-scattered waves occurs and a breakdown of the quantum-beat pattern is observed in the NFS spectrum. 

Recombination fluorescence has been used to study the decay of radical ion pahs generated photolytically.288 Simulation of quantum beats caused by hyperfine interaction in the R and R+ enable the values of hfc to be determined for very short-lived species. In the case of one R excellent agreement with the value of hfc as determined by ESR is reported. The primary reaction in the photolysis of 1-arylalkyl radicals (128) is the heterolytic cleavage of the -halogen (X), generating the radical cation (129).289... 

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... 

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 case the effective laser linewidth is less than the hyperfine splitting(s) excitation will prepare a two-level system. The effect of spin-flips on the coherence in this system will then manifest itself as a 7 ,-type process. No beats are expected in the decay of the optical free induction. With broadband excitation that spans some of the hyperfine splittings spin-flips will be monitored as 7 2-type processes and quantum beats are expected in the photon-echo intensity vs probe delay. Burland et al. also demonstrated the feasibility of optical nutation in this system from which in principle, as from the OFID, the transition dipole could be calculated. 

An obvious limitation on the methods discussed in this review is the need for a choice of radical ion pairs with suitable ESR spectra. Actually, this limitation is due to the insufficient time resolution (quantum beats) or sensitivity (MARY-spectra) of available equipment. Improving these characteristics, one can obtain the spectral information about the systems with a more complex set of hyperfine interactions. Therefore, the further development of observation technique is an urgent task. 

An interesting technique for measuring hyperfine splittings of excited atomic levels by quantum-beat spectroscopy has been reported by Leuchs et al. [876]. The pump laser creates a coherent superposition of HFS sublevels in the excited state that are photoionized by a second laser pulse with variable delay. The angular distribution of photoelectrons, measured as a function of the delay time, exhibits a periodic variation because of quantum beats, reflecting the hfs splitting in the intermediate state. 

Because quantum-beat spectroscopy offers Doppler-free spectral resolution, it has gained increasing importance in molecular physics for measurements of Zee-man and Stark splittings or of hyperfine structures and perturbations in excited molecules. The time-resolved measured signals yield not only information on the dynamics and the phase development in excited states but allow the determination of magnetic and electric dipole moments and of Lande g-factors. 

One example is the measurement of hyperfine quantum beats in the polyatomic molecule propynal HC=CCHO by Huber and coworkers [877]. In order to simplify the absorption spectrum and to reduce the overlap of absorbing transitions from different lower levels, the molecules were cooled by a supersonic expansion (Sect. 4.2). The Fourier analysis of the complex beat pattern (Fig. 7.14) showed that several upper levels had been excited coherently. Excitation with linear and circular polarization with and without an external magnetic field, allowed the analysis of this complex pattern, which is due to singlet-triplet mixing of the excited levels [877, 878]. 

M. Dubs, J. Muhlbach, H. Bitto, R Schmidt, J.R. Huber, Hyperfine quantum beats and Zeeman spectroscopy in the polyatomic molecule propynol CHOCCHO. J. Chem. Rhys. 83,3755 (1985)... 

For measurement of atomic coherence see also "Polarization Selective Detection of Hyperfine Quantum-Beats in Cs", by H. Lehmitz and H. Harde, this symposi+im... 

Because of sub-Doppler resolution, quantum-beat spectroscopy has been used to measure fine or hyperfine structure and Lamb shifts of excited states of neutral atoms and ions [12.38]. 

The method of quantum beats has found application in the measurement of fine structure intervals, polarizabilities, and hyperfine intervals in several species. The basis of the approach is to prepare a coherent superposition of at least two states by pulsed excitation and observe the subsequent... 

Because of the special properties of the exponential function the light decays with the same time constant r as the population decay. The light decay can be followed by a fast detector connected to fast, time-resolving electronics. If the excited state has a substructure, e.g. because of the Zeeman effect or hyperfine structure, and an abrupt, coherent excitation is made, oscillations (quantum beats) in the light intensity will be recorded. The oscillation frequencies correspond to the energy level separations and can be used for structure determinations. We will first discuss the generation of short optical pulses and measurement techniques for fast optical transients. 

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