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arXiv:2009.01682 · Laser Physics Letters

Inverse square root level-crossing quantum two-state model

Tigran A. Ishkhanyan, A. Papoyan, Artur Mikhailovich Ishkhanyan, Claude Leroy

Published Aug 26, 2020• 4 citations
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Abstract

Abstract We introduce a new unconditionally solvable level-crossing two-state model given by a constant-amplitude optical field configuration for which the detuning is an inverse-square-root function of time. This is a member of one of the five families of bi-confluent Heun models. We prove that this is the only non-classical exactly solvable field configuration among the bi-confluent Heun classes, solvable in terms of finite sums of the Hermite functions. The general solution of the two-state problem for this model is written in terms of four Hermite functions of a shifted and scaled argument (each of the two fundamental solutions presents an irreducible combination of two Hermite functions). We present the general solution, rewrite it in terms of more familiar physical quantities and analyze the time dynamics of a quantum system subject to excitation by a laser field of this configuration.

DOI
10.1088/1612-202x/abaccb

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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.