An exactly solvable model of two three-dimensional harmonic oscillators interacting with the quantum electromagnetic field: the Casimir-Polder potential

Abstract

We consider two three-dimensional isotropic harmonic oscillators interacting with the quantum electromagnetic field in the Coulomb gauge and within dipole approximation. Using a Bogoliubov-like transformation, we can obtain transformed operators such that the Hamiltonian of the system, when expressed in terms of these operators, assumes a diagonal form. We are also able to obtain an expression for the energy shift of the ground state, which is valid at all orders in the coupling constant. From this energy shift the nonperturbative Casimir-Polder potential energy between the two oscillators can be obtained. When approximated to the fourth order in the electric charge, the well-known expression of the Casimir-Polder potential in terms of the polarizabilities of the oscillators is recovered.

12 pages

References in corpus (3)

• Dynamical Casimir-Polder energy between an excited and a ground-state atom
• Complex collective states in a one-dimensional two-atom system
• Time-dependent Casimir-Polder forces and partially dressed states

Cited by in corpus (6)

• Dispersion Interactions between Neutral Atoms and the Quantum Electrodynamical Vacuum
• Harmonic oscillator model for the atom-surface Casimir-Polder interaction energy
• Comprehensive Quantum Framework for Describing Retarded and Non-Retarded Molecular Interactions in External Electric Fields
• Is zero-point energy physical? A toy model for Casimir-like effect
• Nonperturbative theory of atom-surface interaction: Corrections at short separations
• Ground State Excitation of an Atom Strongly Coupled to a Free Quantum Field