Nuclear phase coherence

Figure 3. Experimental geometry for dephasing measurements by three-pulse scattering technique. Pump pulses (1 and 2) produce a grating response that diffracts probe pulse (3) into two orders. In grating experiments described in Section III (nuclear phase coherence), t = 0 and probe pulse is incident at the phase-matching angle for Bragg diffraction into only one order.

Spin-spin relaxation is the steady decay of transverse magnetisation (phase coherence of nuclear spins) produced by the NMR excitation where there is perfect homogeneity of the magnetic field. It is evident in the shape of the FID (/fee induction decay), as the exponential decay to zero of the transverse magnetisation produced in the pulsed NMR experiment. The Fourier transformation of the FID signal (time domain) gives the FT NMR spectrum (frequency domain, Fig. 1.7). 

In ESR, it is also customary to classify relaxation processes by their effects on electron and nuclear spins. A process that involves an electron spin flip necessarily involves energy transfer to or from the lattice and is therefore a contribution to Tx we call such a process nonsecular. A process that involves no spin flips, but which results in loss of phase coherence, is termed secular. Processes that involve nuclear spin flips but not electron spin flips are, from the point of view of the electron spins, nonsecular, but because the energy transferred is so small (compared with electron spin flips) these processes are termed pseudosecular. 

In a basic pulsed NMR experiment (for I = 1/2), when a sample is placed in the applied magnetic field (B0), the nuclear spins distribute themselves between parallel and antiparallel positions, according to Boltzmann distribution [Eq. (11)] (Figure 21 A). The number of spins in the parallel position is slightly greater than that in the antiparallel position. At equilibrium, the spins are processing randomly (i.e., lack phase coherence). The populations... 

A further important property of a MQC description is the ability to correctly describe the time evolution of the electronic coefficients. A proper description of the electronic phase coherence is expected to be particularly important in the case of multiple curve-crossings that are frequently encountered in bound-state relaxation dynamics [163]. Within the limits of the classical-path approximation, the MPT method naturally accounts for the coherent time evolution of the electronic coefficients (see Fig. 5). This conclusion is also supported by the numerical results for the transient oscillations of the electronic population, which were reproduced quite well by the MFT method. Similarly, it has been shown that the MFT method in general does a good job in reproducing coherent nuclear motion on coupled potential-energy surfaces. 

If only B0 is applied, the nuclear moments precess without any phase coherence. No resultant component of the magnetization in the x y plane is observed and M, equals M0 (Fig. 1.7(a)). 

The partial recovery of the quantum phase coherence of nuclear dipoles originates from the non-commutative property of the Zeeman energy with the quantum operator which represents the residual interaction after rotating the spins. This rotation has no effect on the magnetisation dynamics when the residual interaction, hHR, is equal to zero. No... 

Relaxation 2,3,6 refers to all processes which regenerate the Boltzmann distribution of nuclear spins on their precession states and the resulting equilibrium magnetisation along the static magnetic field. Relaxation also destroys the transverse magnetisation arising from phase coherence of nuclear spins built up upon NMR excitation. 

There is one other type of relaxation process that must be mentioned at this point. After irradiation ceases and B, disappears, not only do the populations of the m = + and m = states revert to the Boltzmann distribution, but also the individual nuclear magnetic moments begin to lose their phase coherence and return to a random arrangement around the z axis (Figure 2.1a). This latter process, called spin-spin (or transverse) relaxation, causes decay of MJ>y at a rate controlled by the spin-spin relaxation time T2. Normally, T2 is much shorter than T. A little thought should convince you that if T2 < Th then spin-spin (dephasing) relaxation takes place much faster than spin-lattice (Boltzmann distribution) relaxation. 

In general, the motion of M in the rotating frame follows from the classical torque exerted on it by Beff. The effect of an rf pulse is then to tip M away from the z axis and to generate a component in the x y plane. As viewed from the laboratory frame of reference, this component precesses in the xy plane and induces an electrical signal at frequency w in a coil placed in this plane. As the nuclear moments that make up M precess, they lose phase coherence as a result of interactions among them and magnetic field inhomogeneity effects, as described in Section 2.7. Thus Mxy decreases toward its equilibrium value of zero, and the... 

Several recent reviews have presented broad overviews of ultrafast time-resolved spectroscopy [3-6], We shall concentrate instead on a selected, rather small subset of femtosecond time-resolved experiments carried out (and to a very limited extent, proposed) to date. In particular, we shall review experiments in which phase-coherent electronic or, more often, nuclear motion is induced and monitored with time resolution of less than 100 fs. The main reason for selectivity on this basis is the rather ubiquitous appearance of phase-coherent effects (especially vibrational phase coherence) in femtosecond spectroscopy. As will be discussed, nearly any spectroscopy experiment on molecular or condensed-phase systems is likely to involve phase-coherent vibrational motion if the time scale becomes short enough. Since the coherent spectral bandwidth of a femtosecond pulse often exceeds collective or molecular vibrational frequencies, such a pulse may perturb and be perturbed by a medium in a qualitatively different manner than a longer pulse of comparable peak power. The resulting spectroscopic possibilities are of special interest to these reviewers. 

Decoherence in quantum systems is somewhat akin to transverse relaxation in NMR (T2 processes), in which the nuclear spins lose their phase coherence. The proposal that consciousness is somehow connected with collapse of the wavefunc-tion, although intriguing, does not appear to be relevant. 

The detection of energy at this transition frequency is the basis of NMR spectroscopy. The actual detection of NMR signals, however, is made possible through the bulk magnetization (AT) of the nuclear system that arises from the resultant of the individual nuclear magnetic moments that are distributed between the various energy levels. The rotating components (x and y) of p transverse to the direction (z) of B0 at nonresonant equilibrium have no phase coherence and A7x = My = 0,... 

Figure 9. Excitation and relaxation in a population of spins, (a) Before pulse, (b) Induction of phase coherence along y by Hi, and consequent tipping of macroscopic magnetization, M. (c) Dephasing of nuclear magnetic moments by spin-spin relaxation, i.e., M,. = 0. (d) Re-establishment of the Boltzmann distribution (Afj is at its equilibrium value)(a = d).

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