Exactly solvable generalized semi-classical Rabi systems.

Grimaudo R., De Castro A.S.M., Nakazato H., Messina A.

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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 conditions, 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 experimentally intriguing time-dependences of the behaviour of $P_{+}^{-}(t)$ under general conditions. New scenarios of experimental interest originating a Landau-Zener transition are brought to light.