Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Center-of-mass motion of anN-particle atom or ion and the Thomas-Reiche-Kuhn sum rule

C. Baxter

Published Jul 1, 1994• 8 citations
Publisher

Abstract

The Thomas-Reiche-Kuhn sum rule is corrected for the motion of the atomic center of mass, and generalized to include ions. The results are specialized to the case of a two-level atom or ion.Received 18 January 1994DOI:https://doi.org/10.1103/PhysRevA.50.875©1994 American Physical Society

DOI
10.1103/physreva.50.875

Related papers

The Thomas-Reiche-Kuhn sum rule for an atom of N equally spaced energy levels

C. Baxter

The Thomas-Reiche-Kuhn sum rule is determined for an atom consisting of an arbitrary number of discrete, equally spaced eigenenergy levels. This generalization is consistent with a two-level atom and with a usually seen form of the sum rule involving the atomic ground state, and resolves an apparent paradox reported elsewhere.

Journal of Physics B Atomic Molecular and Optical Physics•Dec 14, 1992•9 citations

ELEMENTARY SOLUTIONS OF THE QUANTUM PROBLEM OF THE MOTION OF A PARTICLE IN THE FIELD OF TWO COULOMB CENTERS.

Yu. N. Demkov

•Jan 1, 1968•3 citations

Ion Trapping in Rotating Helium II

Roger L. Douglass

Received 5 November 1964DOI:https://doi.org/10.1103/PhysRevLett.13.791©1964 American Physical Society

Physical Review Letters•Dec 28, 1964•86 citations

Thomas–Reiche–Kuhn (TRK) sum rule for interacting photons

Salvatore Savasta, Omar Di Stefano, Franco Nori

The Thomas-Reiche-Kuhn (TRK) sum rule is a fundamental consequence of the position-momentum commutation relation for an atomic electron, and it provides an important constraint on the transitionmatrix elements for an atom. Here, we propose a TRK sum rule for electromagnetic fields which is valid even in the presence of very strong light- matter interactions and/or optical nonlinearities. While the standard TRK sum rule involves dipole matrix moments calculated between atomic energy levels (in the absence of interaction with the field), the sum rule here proposed involves expectation values of field operators calculated between general eigenstates of the interacting light-matter system. This sum rule provides constraints and guidance for the analysis of strongly interacting light-matter systems and can be used to test the validity of approximate effective Hamiltonians often used in quantum optics.

De Gruyter eBooks•May 25, 2021•1 citation

5. Density Matrix Equations: Atomic Center-of-Mass Motion, Elementary Atom Optics, and Laser Cooling

P. R. Berman, Vladimir S. Malinovsky

Princeton University Press eBooks•Dec 31, 2011•0 citations

Thomas–Reiche–Kuhn (TRK) sum rule for interacting photons

Salvatore Savasta, Omar Di Stefano, Franco Nori

Abstract The Thomas–Reiche–Kuhn (TRK) sum rule is a fundamental consequence of the position–momentum commutation relation for an atomic electron, and it provides an important constraint on the transition matrix elements for an atom. Here, we propose a TRK sum rule for electromagnetic fields which is valid even in the presence of very strong light–matter interactions and/or optical nonlinearities. While the standard TRK sum rule involves dipole matrix moments calculated between atomic energy levels (in the absence of interaction with the field), the sum rule here proposed involves expectation values of field operators calculated between general eigenstates of the interacting light–matter system. This sum rule provides constraints and guidance for the analysis of strongly interacting light–matter systems and can be used to test the validity of approximate effective Hamiltonians often used in quantum optics.

arXiv:2002.02139•Nanophotonics•Nov 18, 2020•17 citations
The Thomas-Reiche-Kuhn sum rule is corrected for the motion of the atomic center of mass, and generalized to include ions. The results are specialized to the case of a two-level atom or ion.Received 18 January 1994DOI:https://doi.org/10.1103/PhysRevA.50.875©1994 American Physical Society
The Thomas-Reiche-Kuhn (TRK) sum rule is a fundamental consequence of the position-momentum commutation relation for an atomic electron, and it provides an important constraint on the transitionmatrix elements for an atom. Here, we propose a TRK sum rule for electromagnetic fields which is valid even in the presence of very strong light- matter interactions and/or optical nonlinearities. While the standard TRK sum rule involves dipole matrix moments calculated between atomic energy levels (in the absence of interaction with the field), the sum rule here proposed involves expectation values of field operators calculated between general eigenstates of the interacting light-matter system. This sum rule provides constraints and guidance for the analysis of strongly interacting light-matter systems and can be used to test the validity of approximate effective Hamiltonians often used in quantum optics.
Abstract The Thomas–Reiche–Kuhn (TRK) sum rule is a fundamental consequence of the position–momentum commutation relation for an atomic electron, and it provides an important constraint on the transition matrix elements for an atom. Here, we propose a TRK sum rule for electromagnetic fields which is valid even in the presence of very strong light–matter interactions and/or optical nonlinearities. While the standard TRK sum rule involves dipole matrix moments calculated between atomic energy levels (in the absence of interaction with the field), the sum rule here proposed involves expectation values of field operators calculated between general eigenstates of the interacting light–matter system. This sum rule provides constraints and guidance for the analysis of strongly interacting light–matter systems and can be used to test the validity of approximate effective Hamiltonians often used in quantum optics.