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Title: Floquet perturbation theory: Applicability of the finite level approximation in different gauges

Abstract

The Floquet perturbation theory represents an important technique for studying the response of atoms or molecules exposed to weak monochromatic fields. In this paper, we discuss an explicit implementation of the Floquet perturbation theory starting from different gauge representations of the matter-light Hamiltonian, namely, from the velocity gauge, the length gauge, and the acceleration gauge. Interestingly, the development of the second-order Floquet perturbation theory in different gauges gives rise to formally different quasienergy corrections, whose mutual equivalence is not self-evident. Nevertheless, our derivation shows how the perturbation formulas associated with different gauges can be converted to one another, provided that a complete basis set of the atomic-molecular electronic states has been used. On the other hand, it turns out that an inappropriate basis set truncation employed for a particular gauge (such as, e.g., the two-level approximation applied within the velocity gauge) may sometimes lead toward completely wrong results. This fact should serve as a warning against an uncautious use of various gauge transformations in practical calculations with a finite basis set.

Authors:
;  [1]
  1. Schulich Faculty of Chemistry and Minerva Center of Nonlinear Physics in Complex Systems, Technion--Israel Institute of Technology, Haifa 32000 (Israel)
Publication Date:
OSTI Identifier:
21020839
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 76; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevA.76.043844; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; ACCELERATION; APPROXIMATIONS; ATOMS; CORRECTIONS; DISTURBANCES; ELECTRONIC STRUCTURE; GAUGE INVARIANCE; HAMILTONIANS; MOLECULES; MONOCHROMATIC RADIATION; PERTURBATION THEORY; PHOTON-ATOM COLLISIONS; PHOTON-MOLECULE COLLISIONS; VELOCITY

Citation Formats

Sindelka, Milan, and Moiseyev, Nimrod. Floquet perturbation theory: Applicability of the finite level approximation in different gauges. United States: N. p., 2007. Web. doi:10.1103/PHYSREVA.76.043844.
Sindelka, Milan, & Moiseyev, Nimrod. Floquet perturbation theory: Applicability of the finite level approximation in different gauges. United States. https://doi.org/10.1103/PHYSREVA.76.043844
Sindelka, Milan, and Moiseyev, Nimrod. 2007. "Floquet perturbation theory: Applicability of the finite level approximation in different gauges". United States. https://doi.org/10.1103/PHYSREVA.76.043844.
@article{osti_21020839,
title = {Floquet perturbation theory: Applicability of the finite level approximation in different gauges},
author = {Sindelka, Milan and Moiseyev, Nimrod},
abstractNote = {The Floquet perturbation theory represents an important technique for studying the response of atoms or molecules exposed to weak monochromatic fields. In this paper, we discuss an explicit implementation of the Floquet perturbation theory starting from different gauge representations of the matter-light Hamiltonian, namely, from the velocity gauge, the length gauge, and the acceleration gauge. Interestingly, the development of the second-order Floquet perturbation theory in different gauges gives rise to formally different quasienergy corrections, whose mutual equivalence is not self-evident. Nevertheless, our derivation shows how the perturbation formulas associated with different gauges can be converted to one another, provided that a complete basis set of the atomic-molecular electronic states has been used. On the other hand, it turns out that an inappropriate basis set truncation employed for a particular gauge (such as, e.g., the two-level approximation applied within the velocity gauge) may sometimes lead toward completely wrong results. This fact should serve as a warning against an uncautious use of various gauge transformations in practical calculations with a finite basis set.},
doi = {10.1103/PHYSREVA.76.043844},
url = {https://www.osti.gov/biblio/21020839}, journal = {Physical Review. A},
issn = {1050-2947},
number = 4,
volume = 76,
place = {United States},
year = {2007},
month = {10}
}