van der Waals interactions between excited atoms in generic environments

We consider the van der Waals force involving excited atoms in general environments, constituted by magnetodielectric bodies. We develop a dynamical approach studying the dynamics of the atoms and the field, mutually coupled. When only one atom is excited, our dynamical theory suggests that for large distances the van der Waals force acting on the ground-state atom is monotonic, while the force acting in the excited atom is spatially oscillating. We show how this latter force can be related to the known oscillating Casimir-Polder force on an excited atom near a (ground-state) body. Our force also reveals a population-induced dynamics: for times much larger that the atomic lifetime the atoms will decay to their ground states leading to the van der Waals interaction between ground-state atoms.

Figure 1

Case (a) is the zero-order approximation: free field and free atom. Case (b) is the next-order approximation: the Lamb shift of an atom due to the emission and reabsorption of a photon. Case (c) is the dispersion interaction between two atoms due to the exchange of two photons.

Figure 2

vdW interaction between one cesium atom in the ground state ($5{}^2{S}_{1/2}$) and an excited rubidium atom ($5{}^2{P}_{1/2}$). The thick line represents the force on rubidium and the dashed one that on cesium.

Figure 3

Body-assisted vdW interaction: the exchanged photons can be reflected by the body's surface.

Figure 4

Population-induced dynamics for the vdW force acting on the excited rubidium atom (thick line). The rubidium atom is in the $5{}^2{P}_{1/2}$ state, while the cesium is in the ground state. The distance between the atoms is $r=10\text{nm}$.