Classes of Exactly Solvable Generalized Semi-Classical Rabi Systems

The exact quantum dynamics of a single spin-1/2 in a generic time-dependent classical magnetic field is investigated and compared with the quantum motion of a spin-1/2 studied by Rabi and Schwinger. The possibility of regarding the scenario studied in this paper as a generalization of that considered by Rabi and Schwinger is discussed and a notion of time-dependent resonance condition is introduced and carefully legitimated and analysed. Several examples help to disclose analogies and departures of the quantum motion induced in a generalized Rabi system with respect to that exhibited by the spin-1/2 in a magnetic field precessing around the $z$-axis. We find that, under generalized resonance condition, the time evolution of the transition probability $P_+^-(t)$ between the two eigenstates of ${\hat{S}}^z$ may be dominated by a regime of distorted oscillations, or may even exhibit a monotonic behaviour. At the same time we succeed in predicting no oscillations in the behaviour of $P_+^-(t)$ under general conditions. New scenarios of experimental interest originating a Landau-Zener transition is brought to light. Finally, the usefulness of our results is emphasized by showing their applicability in a classical guided wave optics scenario.