There is no ultrastrong coupling with photons

Abstract

Theoretical accounts of ultrastrongly coupled light-matter systems commonly assume that it arises from the interaction of an emitter with propagating photon modes supported by a structure, understanding photons as the excitations of the transverse electromagnetic field. This description discards the Coulomb interaction between the emitter and structure charges. Here, we show with a general argument based on electromagnetic constraints that the emitter-photon coupling strength is fundamentally limited. Accordingly, we conclude that the ultrastrong coupling regime cannot be reached with photons. Instead, it must originate from the Coulomb interactions between charges. A further corollary is that the so-called polarization self-energy term does not need to be included. We illustrate our claims by solving an analytical model of the paradigmatic case of an emitter next to a metallic nanosphere. These findings shed light on the fundamental processes underlying ultrastrong coupling, clarify the role of the polarization self-energy term and compel a reevaluation of previous literature.