Exactly Solvable One-Qubit Driving Fields Generated via Nonlinear Equations

Abstract

Using the Hubbard representation for $SU\left(2\right),$ we write the time-evolution operator of a two-level system in the disentangled form. This allows us to map the corresponding dynamical law into a set of nonlinear coupled equations. In order to find exact solutions, we use an inverse approach and find families of time-dependent Hamiltonians whose off-diagonal elements are connected with the Ermakov equation. A physical model with the so-obtained Hamiltonians is discussed in the context of the nuclear magnetic resonance phenomenon.