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Operator-based triple-mode Floquet theory in solid-state NMR
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Image of FIG. 1.
FIG. 1.

Pulse sequence for the basic experiment that will be used to illustrate and validate the results of the trimodal Floquet treatment. In an three-spin system, an initial density operator is generated by a selective pulse. The density operator then evolves for the time under the rf fields with amplitudes and . At the end, the expectation values , , and are detected.

Image of FIG. 2.
FIG. 2.

Intensity plot of the expectation values (a), (b), and (c) for a mixing time of . The simulations were carried out using a heteronuclear spin system and included all dipolar couplings and CSA tensors. The isotropic chemical shifts and the couplings were all set to zero. The MAS frequency was set to and the rf-field amplitudes were varied in a range from . Slices through the 2D plots shown in (a)–(c) along the antidiagonal (d)–(f) and parallel to through (g)–(i).

Image of FIG. 3.
FIG. 3.

Energy-level diagram of a three-spin- system. The energy levels are indicated by horizontal bars with the states written on top. The thin lines indicates the 12 one-quantum transitions. The two arrows indicate the zero-quantum transitions in the subsystem which are allowed under the three-spin operator.

Image of FIG. 4.
FIG. 4.

Numerical simulations of polarization transfer in the TSAR experiment using the same heteronuclear three-spin system as in Fig. 2 taking into account only the heteronuclear dipolar couplings. The spinning frequency was set to . The rf amplitude was set to , and the rf-field amplitude of the spin was varied between 0 and . (a) A simulation using the full time-dependent Hamiltonian is shown in comparison to effective Hamiltonian simulations using (b) only the homonuclear transfer terms and (c) the homonuclear transfer term plus the fictitious-field terms as shown in Eq. (38).


Generic image for table
Table I.

Triplets and the corresponding resonance conditions.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Operator-based triple-mode Floquet theory in solid-state NMR