Exploring the limits of polarization transfer efficiency in homonuclear three spin systems

The limits of polarization transfer efficiency are explored for systems consisting of three isotropically coupled spins 1/2 in the absence of relaxation. An idealized free evolution and control Hamiltonian is studied, which provides an upper limit of transfer efficiency (in terms of transfer amplitude and transfer time) for realistic homonuclear spin systems with arbitrary Heisenberg-type coupling constants J₁₂, J₁₃, and J₂₃. It is shown that optimal control based pulse sequences have significantly improved transfer efficiencies compared to conventional transfer schemes. An experimental demonstration of optimal polarization transfer is given for the case of the carbon spin system of fully ¹³C labelled alanine at 62.5 MHz Larmor frequency.