Second-order coherence calculations

General formulae for intensities of MQ NMR coherences in systems of nuclear spins coupled by the dipole-dipole interactions have been derived. " The second moments of the MQ coherences of zero- and second orders were calculated for infinite linear chains in the approximation of the nearest neighbour interactions. Numerical simulations of intensities of MQ coherences of linear chains were also performed at different times of preparation and evolution periods of MQ NMR experiments. The second moments obtained from the developed theory were compared with the results of the numerical analysis of MQ dynamics. The line width information in MQ NMR experiments has also been discussed. 

We concentrate on the role of quantum interference in the correlation of photons emitted from a coherently driven V-type atom, recently analyzed by Swain et al. [58]. We calculate the normalized second-order two-time correlation function g (R, t R, t + x) for the fluorescent field emitted from a three-level V-type atom driven by a coherent laser field coupled to both atomic transitions. The fluorescence field is observed by a single detector located at a point R = RR, where R is the unit vector in the direction of the observation. 

Quadrupolar Nuclei. - A geometrical description of the quadrupolar interaction has been presented. First- and second-order effects on all transitions were represented by quadrics and quartics. This approach allows a simple and exhaustive description of the Solomon multiple echoes the location of the echoes in the time domain, as well as their nature, is determined without calculation. Experimental evidence of multiple echoes in the case of an Al-O-P cluster is presented. In addition, the selection of double quantum coherences by appropriate phase cycling is presented. DAS and MQ MAS experiments are also described in this particular frame. 

Later, the Fe and Ni LW SEFS spectra were obtained. A comparison between the experimental oscillating structures of Fe and Ni LW SEFS spectra and the corresponding calculated oscillations of p and q types is given in Figure 20. Due to the marked difference between the oscillation periods, it is evident that the oscillating structure of spectra under study is determined by the -oscillation, i.e., by the intermediate-electron coherent scattering in the second-order process. 

To check whether the parameters of our system satisfy coherent three-photon purity , we carried out two calculations with pump pulse duration FWHM = 2ps. The first calculation based on input data from Table la corresponds to the suppression factors FjjT 10 — 10 (depending on F ,). In the second calculation the suppression factors were decreased by three orders of magnitude by decreasing all Fjj in 10 times. Both calculations gave almost the same three-photon absorption coefficient, y (46) (the relative difference Ay/y 7%). This is a direct evidence of negligibly small step-wise absorption processes compared to the coherent three-photon absorption. 

The transformation properties of the odd-parity order parameters imder spatial rotations is reduced to considering the behavior of the quasiparticle states. To leading order in the small ratio kT / so we include the spin-orbit interaction in the calculation of the local atomic basis states, in a second step they are coherently superposed to form extended states. For bands derived from one doubly (Kramers-)degenerate orbital the elements of the point group should act only on the propagation vector. When the Cooper pairs, i.e., the two-particle states, are formed the orbital and spin degrees of freedom can be treated independently. With the spin-orbit interaction already included in the normal state quasiparticles one can use Machida s states derived for vanishing spin-orbit interaction. 

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