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Impact of graphene coating on the atom-plate interaction

Using the recently proposed quantum electrodynamical formalism, we calculate the Casimir-Polder free energies and forces between the ground state atoms of Rb, Na, Cs and He${}^{\ast}$ and the plates made of Au, Si, sapphire and fused silica coated with a graphene sheet. It is shown that the graphene coating has no effect on the Casimir-Polder interaction for metallic plates, but influences significantly for plates made of dielectric materials. The influence of graphene coating increases with decreasing static dielectric permittivity of the plate material and the characteristic frequency of an atomic dynamic polarizability. Simple analytic expressions for the classical limit of the Casimir-Polder free energy and force between an atom and a graphene-coated plate are obtained. From the comparison with the results of numerical computations, the application region of these expressions is determined.