Abstract
AbstractDressed 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. Moreover, 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.
Highlights
Quantum emitters (“atoms”) coupled to structured and/or low-dimensional photonic environments are an important paradigm of quantum optics and nanophotonics
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
We show that the resolvent operator can be expressed in a compact form structurally analogous to that arising in the standard impurity problem
Summary
Quantum emitters (“atoms”) coupled to structured and/or low-dimensional photonic environments are an important paradigm of quantum optics and nanophotonics. For emitters energetically lying within photonic bandgaps, such effective second-order interactions can be dissipationless These are usually explained in terms of mediating dressed bound states (BSs) [10,11,12,13,14,15]. A natural question is to what extent the emitterimpurity analogy holds, in particular whether it can be formalized in a framework independent of the bath Hamiltonian and applied to the calculation of both bound and unbound dressed states (the latter ones rule photon scattering processes). We show that the resolvent operator (or Green function) can be expressed in a compact form structurally analogous to that arising in the standard impurity problem This condenses the effect of atom-photon coupling in a single rank-one projector, allowing for a unified treatment of several kinds of dressed states (either bound and unbound). The framework is extended to the case that more than one emitter is present and used to derive a general expression of dissipationless effective Hamiltonians (mentioned above), which explicitly connects the interatomic potential to overlapping single-atom dressed states independently of the specific photonic bath
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