Level crossings and new exact solutions of the two-photon Rabi model
Quantum Physics
2020-05-08 v1 Mathematical Physics
math.MP
Abstract
An infinite family of exact solutions of the two-photon Rabi model was found by investigating the differential algebraic properties of the Hamiltonian. This family corresponds to energy level crossings not covered by the Juddian class, which is given by elemetary functions. In contrast, the new states are expressible in terms of parabolic cylinder or Bessel functions. We discuss three approaches for discovering this hidden structure: factorization of differential equations, Kimura transformation, and a doubly-infinite, transcendental basis of the Bargmann space.
Keywords
Cite
@article{arxiv.1910.11037,
title = {Level crossings and new exact solutions of the two-photon Rabi model},
author = {Andrzej J. Maciejewski and Tomasz Stachowiak},
journal= {arXiv preprint arXiv:1910.11037},
year = {2020}
}
Comments
Accepted for publication in Journal of Physics A; 17 pages, 1 color figure