2020/02/29 by Salvatore Savasta, Omar Di Stefano, Franco Nori
Engineering · Physics and Astronomy · #Commutation #Constraint (computer-aided design) #Dipole #Eigenvalues and eigenvectors #Electromagnetic field #Matrix (chemical analysis) #Orbital Angular Momentum in Optics #Photon #Plasmonic and Surface Plasmon Research #Quantum #Strong Light-Matter Interactions #Sum rule in quantum mechanics #quant-ph
paper · pdf · doi:10.1515/nanoph-2020-0433
published as Nanophotonics 465 10 2021 · 22 pages, 4 figures
openalex created_date 2020/02/14 · arxiv created 2020/11/03 · openalex publication_date 2020/11/18 · arxiv updated 2021/03/23 · openalex updated_date 2026/08/06
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.