Interaction of a Bose-Einstein condensate with a surface: perturbative S-matrix approach

TL;DR

This paper develops a perturbative S-matrix approach to calculate the collective Casimir-Polder interaction between a Bose-Einstein condensate and a surface, accounting for many-body effects and spatial delocalization.

Contribution

It introduces a systematic diagrammatic perturbation theory for the condensate-surface interaction, extending single-atom results to many-body systems with corrections from atom-atom interactions.

Findings

Interaction energy scales with the number of condensate atoms.

Atom-atom interactions cause shifts in atomic transition energies.

Spatial delocalization influences the interaction strength.

Abstract

We derive an expression for the collective Casimir-Polder interaction of a trapped gas of condensed bosons with a plane surface through the coupling of the condensate atoms with the electromagnetic field. A systematic perturbation theory is developed based on a diagrammatic expansion of the electromagnetic self-energy. In the leading order, the result for the interaction-energy is proportional to the number of atoms in the condensate mode. At this order, atom-atom interactions and recoil effects lead to corrections compared to the single-atom theory, through shifts of the atomic transition energies. We also discuss the impact of the spatial delocalization of the condensate mode.