Synthesis of matched magnetic fields for controlled spin precession

The shaping of magnetic fields is important in many areas of physics, including magnet shimming, electromagnetic traps, magnetic domain switching, and controlled spin precession in nuclear magnetic resonance (NMR). We examine the method of target field matching by orthogonal projection and its application to NMR, whereby the phase of nuclear spins in a strongly inhomogeneous field is corrected through stroboscopic ac irradiation using matching fields. Three-dimensional shaping of static and ac fields can restore the spectral resolution by orders of magnitude using simple linear combinations of a small number of independent sources. Results suggest the possibility of substantially pushing the current limits of high-resolution NMR spectroscopy in weak and inhomogeneous fields. We also discuss conditions under which concomitant gradient effects are important in high magnetic fields and the geometric-phase errors they introduce during precession in ac fields.