Recoil momentum of an atom absorbing light in a gaseous medium and the Abraham-Minkowski debate

We discuss a fundamental question regarding the Abraham-Minkowski debate about the momentum of light in a medium: If an atom in a gas absorbs a photon, what is the momentum transferred to it? We consider a classical model for the internal degrees of freedom of the absorbing atom, computing the absorbed energy and momentum using the Lorentz force law due to the microscopic electromagnetic fields. Each non-absorbing atom from the gas is treated as a dielectric sphere, with the set of atoms forming a linear, dielectric, non-magnetic, and non-absorbing medium with a refractive index $n$ close to one. Our numerical results indicate that if the atoms are classically localized, the average absorbed momentum increases with $n$, but is smaller than Minkowski's momentum $np_0$, $p_0$ being the photon momentum in vacuum. However, experiments performed with Bose-Einstein condensates [Phys. Rev. Lett. $\mathbf{94}$, 170403 (2005)] are consistent with the atom absorbing Minkowski's momentum. We argue that there is no contradiction between these results since, in a Bose-Einstein condensate, the atoms are in a quantum state spatially superposed in a relatively large volume, forming a ``continuous'' medium. In this sense, the experimental verification of an atomic momentum recoil compatible with Minkowski's momentum would be a quantum signature of the medium state.