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 matterlight Hamiltonian, namely, from the velocity gauge, the length gauge, and the acceleration gauge. Interestingly, the development of the secondorder Floquet perturbation theory in different gauges gives rise to formally different quasienergy corrections, whose mutual equivalence is not selfevident. 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 atomicmolecular 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 twolevel 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:

 Schulich Faculty of Chemistry and Minerva Center of Nonlinear Physics in Complex Systems, TechnionIsrael 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 10502947
 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; PHOTONATOM COLLISIONS; PHOTONMOLECULE 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 matterlight Hamiltonian, namely, from the velocity gauge, the length gauge, and the acceleration gauge. Interestingly, the development of the secondorder Floquet perturbation theory in different gauges gives rise to formally different quasienergy corrections, whose mutual equivalence is not selfevident. 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 atomicmolecular 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 twolevel 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 = {10502947},
number = 4,
volume = 76,
place = {United States},
year = {2007},
month = {10}
}