Iterative Maps for Bistable Excitation of Two-Level Systems

Iterative maps on SO (3) with two stable fixed points are described. These generate bistable spectroscopic excitation sequences for isolated two-level systems. From such sequences, tailored population inversion over specific ranges of parameters such as the resonance frequency or radiation amplitude can be obtained. The ideas developed here suggest ways of designing tailored excitation sequences useful in spatially selective NMR, spin decoupling, $\mathrm{nk}$-quantum selective multiple-quantum NMR, and isotope-selective zero-field NMR.