Harmonic oscillator model for the atom-surface Casimir-Polder interaction energy

TL;DR

This paper introduces an exact, non-perturbative method using a harmonic oscillator model and Bogoliubov transformation to compute the atom-surface Casimir-Polder interaction energy, recovering known results and enabling analysis of complex systems.

Contribution

It presents a novel exact approach for calculating Casimir-Polder energies using a harmonic oscillator model and Bogoliubov transformation, applicable beyond perturbation theory.

Findings

Derived non-perturbative expressions for ground-state energy.

Recovered known lowest-order Casimir-Polder results.

Discussed advantages for complex systems where perturbation theory fails.

Abstract

In this paper we consider a quantum harmonic oscillator interacting with the electromagnetic radiation field in the presence of a boundary condition preserving the continuous spectrum of the field, such as an infinite perfectly conducting plate. Using an appropriate Bogoliubov-type transformation we can diagonalize exactly the Hamiltonian of our system in the continuum limit and obtain non-perturbative expressions for its ground-state energy. From the expressions found, the atom-wall Casimir-Polder interaction energy can be obtained, and well-know lowest-order results are recovered as a limiting case. Use and advantage of this method for dealing with other systems where perturbation theory cannot be used is also discussed.