Journal
NANOPHOTONICS
Volume 10, Issue 17, Pages 4251-4259Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/nanoph-2021-0490
Keywords
photonic band-gap materials; quantum optics; waveguide-QED
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Funding
- MUR through project PRIN Project [2017SRN-BRK QUSHIP]
- Government of the Russian Federation [074-02-2018-330 (2)]
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The paper introduces a compact formulation of the resolvent-based theory for calculating atom-photon dressed states, establishing a connection with the standard impurity problem in condensed matter and solving many previously unspecified properties. It also extends the framework to multiple emitters, deriving a general expression of dissipationless effective Hamiltonians explicitly featuring the overlap of single-emitter dressed bound states.
Dressed states forming when quantum emitters or atoms couple to a photonic bath underpin a number of phenomena and applications, in particular nonradiating effective interactions occurring within photonic bandgaps. Here, we present a compact formulation of the resolvent-based theory for calculating atom-photon dressed states built on the idea that the atom behaves as an effective impurity. This establishes an explicit connection with the standard impurity problem in condensed matter. More -over, it allows us to formulate and settle - independently of the bath Hamiltonian - a number of properties previously known only for specific models or not entirely formalized. The framework is next extended to the case of more than one emitter, which is used to derive a general expression of dissipationless effective Hamiltonians explicitly featuring the overlap of single-emitter dressed bound states.
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