Classes of Exactly Solvable Generalized Semi-Classical Rabi Systems

TL;DR

This paper explores exactly solvable models of generalized semi-classical Rabi systems, revealing new resonance behaviors, transition dynamics, and potential experimental applications in quantum and classical optics.

Contribution

It introduces a class of exactly solvable generalized Rabi models with time-dependent resonance conditions and analyzes their quantum dynamics and potential experimental implications.

Findings

Under generalized resonance, transition probabilities show distorted oscillations or monotonic behavior.

No oscillations occur in transition probabilities under certain general conditions.

The results are applicable to classical guided wave optics scenarios.

Abstract

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.