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We consider the time-dependent resonance interaction energy between twoidentical atoms, one in the ground state and the other in an excited state, andinteracting with the vacuum electromagnetic field, during a nonequilibriumsituation such as the dynamical atomic self-dressing process. We suppose thetwo atoms prepared in a correlated, symmetric or antisymmetric, state. Sincethe atoms start from a nonequilibrium conditions, their interaction energy istime dependent. We obtain, at second order in the atom-field coupling, ananalytic expression for the time-dependent resonance interaction energy betweenthe atoms. We show that this interaction vanishes when the two atoms areoutside the light-cone of each other, in agreement with relativistic causality,while it instantaneously settles to its stationary value after time $t=R/c$($R$ being the interatomic distance), as obtained in a time-independentapproach. We also investigate the time-dependent electric energy density in thespace around the two correlated atoms, in both cases of antisymmetric(subradiant) and symmetric (superradiant) states, during the dressing processof our two-atom system. We show that the field energy density vanishes inpoints outside the light-cone of both atoms, thus preserving relativisticcausality. On the other hand, inside the light-cone of both atoms, the energydensity instantaneously settles to its stationary value. Specifically, forpoints at equal distance from the two atoms, we find that it vanishes if thetwo atoms are prepared in the antisymmetric (subradiant) state, while it isenhanced, with respect to the case of atoms in a factorized state, in thesymmetric (superradiant) state. The physical meaning of these results isdiscussed in detail in terms of interference effects of the field emitted bythe two atoms.

Time-dependent resonance interaction energy between two entangled atoms under non-equilibrium conditions