Canonical quantum plasmonics for finite nanostructures: Exact solution in one dimension

As opposed to what is widely described in literature, quantum plasmon-polariton excitations are characterized by two families of creation and annihilation operators associated by continuity with the free electromagnetic field and the medium oscillators. In this paper, we elaborate the quantum plasmonics theory using the canonical quantization technique by means of the Lippmann-Schwinger equation: We derive (i) the polaritonic electromagnetic field, modified by the presence of a finite-size medium, expressed in terms of the classical Green function satisfying the Sommerfeld outgoing radiation condition, and (ii) the imaginary Green's function identity, which both complement the forms of bulk models used in literature. We prove the standard Purcell formula of a two-level quantum emitter, located near or inside the medium, emerging via a compensation of two terms in the respective expressions of the electric field and the imaginary Green's function identity, that are not present in a bulk configuration. These results provide a solid foundation for further developments with suitable physical interpretations of quantum nanotechnologies with dielectric or metallic structures in interaction with quantum emitters.