Analytical unitary bounds on quantum dynamics: Design of optimum NMR experiments in two-spin-[FRACTION SHAPE="CASE"][NUM]1[/NUM][DEN]2[/DEN][/FRACTION] systems.

We report analytical solutions to the unitary bound problem for coherence/polarization transfer in IS two-spin-[FRACTION SHAPE="CASE"][NUM]1[/NUM][DEN]2[/DEN][/FRACTION] systems by means of unitary operations. Theoretical upper bounds for the transfer efficiency along with the associated optimum transformation operators are obtained analytically by decomposing the unitary operator as a product of exponentials in the special unitary Lie group SU(4). Addressing NMR spectroscopy as a specific example, the method is demonstrated for the non-Hermitian transfers I[sup -]→S[sup -] and 2I[sup -]S[sub z]→S[sup -] being relevant for heteronuclear single-quantum coherence (HSQC) experiments as well as the double- to single-quantum transfer I[sup -]S[sup -]→I[sup -]S[sup β]+I[sup β]S[sup -] being representative for coherence-order and spin-state-selective transfer in INADEQUATE CR experiments. Furthermore, using a Lagrangian function approach it is demonstrated how the method enables analytical description of two-dimensional bounds for I[sub z]→S[sub z] cross polarization. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]