Rephasing

Figure Al.6.23. Schematic representation of dephasing and reversal on a race track, leading to coherent rephasing and an echo of the starting configuration. From Phys. Today, (Nov. 1953), front cover.

Figure Al.6.25. Modulus squared of tire rephasing, (a), and non-rephasing, R., (b), response fiinetions versus final time ifor a near-eritieally overdamped Brownian oseillator model M(i). The time delay between the seeond and third pulse, T, is varied as follows (a) from top to bottom, J= 0, 20, 40, 60, 80, 100,...

This is followed by two field actions which again create a vibrational coherence but, now, with opposite phase to the first coherence. Hence one obtains a partial rephasing, or echo, of the macroscopic polarization. The final field action creates the seventh order optical polarization which launches the signal field (the eighth field). Just as for the spin echo in NMR or the electronic echo in 4WM, the degree of rephasing (tlie... 

Figure Bl.3.8. A WMEL diagram for die three-colour fifth order qiiasi-Ramaii echo . As usual, the first pair of field actions creates the Raman coherence which is allowed both to dephase and walk off with time. This is followed by a second pair of field actions, which creates a different but oppositely phased Raman coherence (now hf) to the first. Its frequency is at oi - oij = Provided that frequencies are identified with an inliomogeneous distribution that is similar to those of the frequencies, then a quasi-rephasing is possible. The fifth field action converts the newly rephased Raman polarization into the quasi-echo at co = 2(b, — CO, = CO, + CO,...

Fig. 21. Timing scheme of a STEAM sequence for diffusion measurements with a pair of diffusion weighting dephasing/rephasing gradients. Parameters 8, A, and A determine the diffusion weighting (h-value).

Fig. 1. Time sequence of the three-pulse single- or dual-frequency (shaded and unshaded) heterodyned 2D-IR experiments. (A) Rephasing (B) Nonrephasing sequences. The signal is observed in the k2 +k3 -ki direction.

Fig. 4. Locations of the diagonal and off-diagonal peaks in the 2D-IR spectra in the rephasing (upper) and nonrephasing (lower) quadrant of (to, to,)- (A) single-frequency (B) two pulses one centered at coi and the other at ton- D and d are the diagonal and off-diagonal anharmonicities, respectively. The cross peaks near (I, II) and the (II, II-D) peaks are omitted for clarity.

Fig. 6. Real parts of dual-frequency 2D-IR spectra ofNMA. (A) rephasing (B) nonrephasing.

Fig. 7. Measured and simulated absolute magnitude 2D-IR rephasing spectra of a 25mer a-helix with double isotope substitutions denoted as [ 3C= 60, l3C= 80]. (A) [12,13], (B) [11,13], Experimental condition D20-phosphoric acid buffer at 0° C. (C) and (D) are corresponding simulations.

Figure 15. Feynman diagrams for r > 0 where rephasing is possible and r < 0 where rephasing is not possible. Note that for r > 0 the density matrix element during r and ( are complex conjugate of each other, but they have the same phase for r < 0.

If a sample contains equivalent nuclei A (13C) subject to spin-spin coupling with nuclei X ( H), the transverse magnetization arises from two or more Larmor frequencies, depending on the multiplicity. The corresponding magnetization vectors periodically rephase and dephase with the field vector B, as in the off-resonance case with one Larmor frequency (Section 2.4.1). The FID signal is thus modulated by the frequency of the coupling constant JAX [7,13] as illustrated in Fig. 2.5 (a) for hexadeuteriodimethyl sulfoxide. 

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