Thomas–Reiche–Kuhn (TRK) sum rule for interacting photons
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Nov 18, 2020
- Source ID
- 10.1515/nanoph-2020-0433
Entities
People
- Franco Nori
- Omar Di Stefano
- Salvatore Savasta
Organizations
- Army Research Office
- Foundational Questions Institute
- Japan Science and Technology Agency
- Japan Society for the Promotion of Science
- NTT Research
- Silicon Valley Community Foundation
- University of Messina
- University of Michigan