Four-parametric generalization of the second Demkov-Kunike two-state model

Abstract

We introduce a new time-dependent level-crossing model that describes a quantum two-state system subjected to a constant-amplitude laser field. In this configuration, which presents a four-parametric generalization of the three-parametric second Demkov-Kunike level-crossing model, the frequency detuning changes within a finite range and the resonance crossing generally occurs asymmetrically in time with respect to the crossing point. The general solution to this problem can be written as a linear combination with arbitrary constant coefficients of two independent generalized hypergeometric functions of Clausen, each of which can be presented as a linear combination of two ordinary hypergeometric functions. We analyze the asymptotes of the solution in terms of the quasi-energies and compute the final transition probability for the scenario where the system starts in the first quasi-energy state.