Selective spin inversion in nuclear magnetic resonance and coherent optics through an exact solution of the Bloch-Riccati equation

Abstract

An analytical solution of the Bloch equations is presented using as a driving function a complex hyperbolic secant pulse. The solution indicates that, under the appropriate conditions, the use of such a pulse creates a highly selective population inversion which, above a critical threshold, is independent of pulse (irradiating $B_1$ field) amplitude and hence $B_1$ field homogeneity. This result is shown to be in excellent agreement with experiment, and as an aid to comprehension, analogies to adiabatic rapid passage and self-induced transparency are drawn.