Journal
NANOPHOTONICS
Volume 10, Issue 1, Pages 465-476Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/nanoph-2020-0433
Keywords
cavity QED; quantum optics; sum rules
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Funding
- NTT Research
- Japan Science and Technology Agency (JST) (CREST) [JPMJCR1676]
- Japan Society for the Promotion of Science (JSPS) (KAKENHI) [JP20H00134]
- Japan Society for the Promotion of Science (JSPS) (JSPS-RFBR) [JPJSBP120194828]
- Asian Office of Aerospace Research and Development (AOARD)
- Foundational Questions Institute Fund (FQXi), a donor advised fund of the Silicon Valley Community Foundation [FQXi-IAF19-06]
- Army Research Office (ARO) [W911NF1910065, W911NF-18-1-0358]
- U.S. Department of Defense (DOD) [W911NF1910065] Funding Source: U.S. Department of Defense (DOD)
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The study proposes a TRK sum rule for electromagnetic fields that remains valid even in the presence of strong light-matter interactions or optical nonlinearities. Unlike the standard TRK sum rule, this proposed rule involves expectation values of field operators calculated between general eigenstates of the interacting light-matter system.
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.
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