2005/08/03 by Francesco Ciccarello, F. Ciccarello, E. Karpov +3 · 1 citation
Physics and Astronomy · #Mechanical and Optical Resonators #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Applications #quant-ph
paper · pdf · doi:10.1103/physreva.72.052106
published as Physical Review A 72, 052106 (2005) · 12 pages
arxiv created 2005/08/03 · openalex publication_date 2005/11/08 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We consider two three-dimensional isotropic harmonic oscillators with the same frequency and interacting with the quantum electromagnetic field in the Coulomb gauge and within dipole approximation. Using a Bogoliubov-type 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 far zone Casimir--Polder potential in terms of the polarizabilities of the oscillators is recovered.