The Casimir-Polder effect for an approximate Pauli-Fierz model: the atom plus wall case

TL;DR

This paper analyzes the Casimir-Polder effect for a hydrogen atom near a conducting wall using a simplified quantum electromagnetic model, revealing how quantum fluctuations modify the interaction decay from $L^{-3}$ to $L^{-4}$.

Contribution

It introduces a Pauli-Fierz model with dipole approximation to explicitly derive the retardation effects in atom-wall interactions.

Findings

Interaction decay changes from $L^{-3}$ to $L^{-4}$ due to quantum fluctuations.

The model captures the transition from van der Waals to Casimir-Polder regimes.

Quantum electromagnetic fluctuations weaken the atom-wall interaction at large distances.

Abstract

We study a system composed of a hydrogen atom interacting with an infinite conductor wall. The interaction energy decays like $L^{-3}$, where $L$ is the distance between the atom and the wall, due to the emergence of the van der Waals forces. In this paper we show how, considering the contributions from the quantum fluctuations of the electromagnetic field, the interaction is weakened to a decay of order $L^{-4}$ giving rise to the retardation effects which fall under the name of Casimir-Polder effect. The analysis is done by studying a suitable Pauli-Fierz model associated to the system, in dipole approximation and reduced to the interaction with 0 and 1 photon.