Quantum-beat pattern

Fluctuations of the EFG cause a dephasing of the originally coherent waves which affects the quantum-beat pattern (as described for Mb02 in Sect. 9.4.3) and... 

Fig. 9.16 Time-dependent NFS of [Fe(tpa)(NCS)2] recorded at 108 K. The two curves represent comparison of a coherent vs incoherent superposition of the scattering from 50 % LS and 50 % HS iron(II) characterized by their corresponding quantum beat pattern. The effective thickness of the sample was =18. (Taken from [42])...

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. 

Fig. 9.12 (a) NFS spectra of FC/DBP with quantum beat and dynamical beat pattern, (b) Temperature-dependent /-factor. The solid line is a fit using the Debye model with 0D = 41 K below 150 K. Above, a square-root term / - V(Tc - T)/Tc was added to account for the drastic decrease of /. At Tc = 202 K the glass-to-liquid transition occurs. (Taken Ifom [31])... 

When the nuclei are subjected to an electrical quadrupole interaction, the NFS pattern shows quantum beats with a single frequency corresponding to the energy difference between the sub-levels of the exited state (AEq), which is equal to the... 

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... 

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. 

Figure 7a shows that there exists a longer time modulation (about 2 ps) in the chromophore population. The origin of this modulation can be directly traced to the i3 mode, the population of which displays the same evolution pattern as shown in Figure 7c. In this figure, we have compared the Aj and N3 average quantum numbers. It can be seen that these populations vary out of phase, indicating a resonance between the v, and v3 modes. From the quantum beat period, we expect a resonance between two states separated by 15 cm 1 as we noticed previously, the states with energies 16,169 cm 1 and 16,152 cm-1 have an important contribution from the 3 mode. Finally the N2, N4, and N6 populations, shown in Figure 7d, display a monotonic increase over the 15-ps interval, apart from modulations due to the N -N5 and Nt-N2 resonances. The overall relaxation from the 6v,)° mode is displayed in Figure 8.

Formally, a pattern of quantum beats can be characterized by the parameters such as the set of oscillation fi-equencies, oscillation decay time, the phase shift of oscillations, and, finally, their amplitude. Each parameter contains useful information about the processes in radiation spurs. The oscillation frequencies correspond to the splittings in the ESR spectrum of radical ions. The decay of oscillations contains information about spin relaxation times. The phase shift reflects the time delay of pair formation from its precursor. Finally, the amplitude of oscillating component is determined by the fraction of spin correlated pairs. 

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]. 

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. 

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