Theoretical studies of many-particle systems with long-range interactions find remarkable new features and concepts due to their non-additivity, e.g. inequivalence between statistical ensembles, negative specific heat and slow relaxation times to equilibrium. However, these exciting predictions are still awaiting experimental verification. We show that atoms subject to laser radiation may form a non-additive many-body system on account of their long-range interactions, when the atoms are trapped in the vicinity of a fiber with Bragg grating. The dynamics of this system conforms to a prominent model of statistical physics which exhibits slow relaxation. This suggests the possibility of using laser-illuminated atoms to study the characteristics of non-additive systems in a controlled setups.