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

Nanophotonics

article

Salvatore Savasta¹  Omar Di Stefano¹  Franco Nori² 

[1] Dipartimento di Scienze Matematiche e Informatiche, Università di Messina;Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research;Physics Department, The University of Michigan

关键词: cavity QED;    quantum optics;    sum rules;   

DOI  :  10.1515/nanoph-2020-0433

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

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.

【 授权许可】

CC BY