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We consider two three-dimensional isotropic harmonic oscillators interactingwith the quantum electromagnetic field in the Coulomb gauge and within dipoleapproximation. Using a Bogoliubov-like transformation, we can obtaintransformed operators such that the Hamiltonian of the system, when expressedin terms of these operators, assumes a diagonal form. We are also able toobtain an expression for the energy shift of the ground state, which is validat all orders in the coupling constant. From this energy shift thenonperturbative Casimir-Polder potential energy between the two oscillators canbe obtained. When approximated to the fourth order in the electric charge, thewell-known expression of the Casimir-Polder potential in terms of thepolarizabilities of the oscillators is recovered.Comment: 12 page

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

Exactly solvable model of two three-dimensional harmonic oscillators interacting with the quantum electromagnetic field: The far-zone Casimir-Polder potential