Polarization transfer experiments in high-resolution NMR spectroscopy

Symmetry constraints on spin dynamics: Application to hyperpolarized NMR

“…There are fundamental bounds on the coherent transformations of spin density operator components, associated with the conservation of eigenvalues under unitary transformation [1,2,3,4]. If the eigenvalue spectra of the two operators match, a complete transformation of one operator component into another is possible.…”

“…In a series of papers, Sørensen and co-workers defined the limiting value of the transformation amplitude for one density operator component into another. These results were applied to a variety of NMR problems, including polarization transfer between spin species [1,2,3,4,5,6], and cross-polarization in solids [7,8,6]. Extensions to non-Hermitian operators and non-unitary dissipative evolution were developed [9,10,11].…”

“…To facilitate discussion of this topic, the theory of unitary bounds in the presence of symmetry, as developed by Sørensen and co-workers [1,2,3,4,5,6,7,8,9,10,12] is reviewed and reformulated with a revised notation, and combined with a more detailed discussion of spin permutation symmetry.…”

Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms

“…Many applications in NMR spectroscopy [34,35] and NMR quantum computing [36,37,38] require unitary transformations of the form…”

Broadband geodesic pulses for three spin systems: time-optimal realization of effective trilinear coupling terms and indirect SWAP gates

“…In the context of NMR polarization-transfer experiments, methods for creating such effective trilininear Hamiltonians have been developed and used for many years (6,7). One approach to create such effective Hamiltonians is based on the decoupling of certain interactions during the pulse sequence (3,8,9).…”