Technological development in the implementation of optical resonatorsstrongly coupled to two-level systems has made it increasingly easy to accessnon-perturbative regimes known as ultra or deep strong coupling, where thecoupling rate is of the order of the frequency of the bare modes and counterrotating terms in the Hamiltonian play a relevant role. In this work, weaddress the adequacy of the single-mode Rabi model to describe non-perturbative light-matter coupling. In the case of resonators with harmonicspectra, we discuss how the single- mode approximation yields unphysicalresults leading to superluminal signalling. We show that the multi-modedescription of the field, necessary to account for light propagation at finitespeed, yields physical observables, such as transition energies or populationdynamics, that differ radically from their single-mode counterpart already inthe ultrastrong coupling regime. Our analysis of the multi-mode Rabi model alsoreveals phenomena of fundamental interest on the dynamics of the electric fieldinside the cavity, where a free photonic wavefront and a bound state of virtualphotons are shown to coexist.
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