Resolution of superluminal signalling in non-perturbative cavity quantum electrodynamics

Recent technological developments have made it increasingly easy to access the non-perturbative regimes of cavity quantum electrodynamics known as ultrastrong or deep strong coupling, where the light–matter coupling becomes comparable to the bare modal frequencies. In this work, we address the adequacy of the broadly used single-mode cavity approximation to describe such regimes. We demonstrate that, in the non-perturbative light–matter coupling regimes, the single-mode models become unphysical, allowing for superluminal signalling. Moreover, considering the specific example of the quantum Rabi model, we show that the multi-mode description of the electromagnetic field, necessary to account for light propagation at finite speed, yields physical observables that differ radically from their single-mode counterparts already for moderate values of the coupling. Our multi-mode analysis also reveals phenomena of fundamental interest on the dynamics of the intracavity electric field, where a free photonic wavefront and a bound state of virtual photons are shown to coexist.