We compare the predictions of the fundamentally motivated minimal coupling ( p • Â) and the ubiquitous dipole coupling ( x • Ê) in the light-matter interaction. By studying the light-matter interaction for hydrogen-like atoms we find that the dipole approximation cannot be a-priori justified to analyze the physics of vacuum excitations (a very important phenomenon in relativistic quantum information) since a dominant wavelength is absent in those problems, no matter how small (as compared to any frequency scale) the atom is. Remarkably, we show that the dipole approximation in those regimes can still be valid as long as the interaction time is longer than the light-crossing time of the atoms, which is a very reasonable assumption. We also highlight some of the subtleties that one has to be careful with when working with the explicitly gauge noninvariant nature of the minimal coupling and we compare it with the explicitly gauge invariant dipole coupling.their atoms to 2-level systems.Note our units are = c = 0 = 1. On some occasions these constants will be explicitly restored for clarity.

We present new results on the causality violations introduced by the rotating wave approximation commonly used in quantum optics and high-energy physics. We find that the causality violations and faster-than-light signalling induced by the approximation have 'fat tails', i.e., they are polynomially decaying with the distance from the light-cone of the emitter. Furthermore, we also show that the fundamental problems with the incompatibility between the approximation and relativity are not cured even in the long interaction time regime (where the approximation is often taken). This renders the approximation unsuitable for any regime where we are concerned about relativistic causality and information transmission via the electromagnetic field.

We use quantum energy teleportation in the light-matter interaction as an operational means to create quantum field states that violate energy conditions and have negative local stress-energy densities. We show that the protocol is optimal in the sense that it scales in a way that saturates the quantum interest conjecture.