Parabolic level crossing models

Kalle‐Antti Suominen, B. M. Garraway, Stig Stenholm

A. A. Suzko, E. P. Velicheva

Chon‐Fai Kam, Yang Chen

Chon‐Fai Kam, Yang Chen

Abstract We study the dynamics of a two-level crossing model with a parabolic separation of the diabatic energies. The solutions are expressed in terms of the tri-confluent Heun equations—the generalization of the confluent hypergeometric equations. We obtain analytical approximations for the state populations in terms of Airy and Bessel functions. Applicable expressions are derived for a large part of the parameter space. We also provide simple formulas which connect local solution in different time regimes. The validity of the analytical approximations is shown by comparing them to numerical simulations.

Jaakko Lehto, Kalle‐Antti Suominen

Level crossing models for two-state quantum systems are applicable to a wide variety of physical problems. We address the special case of level glancing, i.e., when energy levels reach a degeneracy at a specific point of time, but never actually cross. The simplest model with such behavior is the parabolic model, and its generalizations, which we call superparabolic models. We discuss their basic characteristics, complementing the previous work on the related nonlinear crossing models [Vitanov and Suominen, Phys. Rev. A 59, 4580 (1999)].

Lehto J, Kalle‐Antti Suominen

Level crossing models for two-state quantum systems are applicable to a wide variety of physical problems. We address the special case of level glancing, i.e., when energy levels reach a degeneracy at a specific point of time, but never actually cross. The simplest model with such behavior is the parabolic model, and its generalizations, which we call superparabolic models. We discuss their basic characteristics, complementing the previous work on the related nonlinear crossing models [Vitanov and Suominen, Phys. Rev. A 59, 4580 (1999)].