Asymmetric Version of the Second Demkov–Kunike Level-Crossing Model

Abstract

We present a novel time-dependent two-state model that describes a constant-amplitude level-crossing field configuration, where the frequency detuning varies within a finite interval. A distinctive feature of this configuration is that the resonance crossing always occurs asymmetrically in time, making it an asymmetric version of the second Demkov-Kunike model. The general solution of the problem is expressed in terms of two independent irreducible linear combinations of the Gauss hypergeometric functions. We analyze the asymptotes of the solution in terms of corresponding quasi-energies and calculate the final transition probability in the case when the system starts from the first quasi-energy state.