Dressing the Lorentz atom

TL;DR

This paper analyzes how the electromagnetic vacuum influences a harmonically bound electron, deriving an effective one-dimensional model and analytically determining the ground state to understand the atom's behavior.

Contribution

It introduces a simplified one-dimensional model of a Lorentz atom coupled to the vacuum field and analytically characterizes its ground state.

Findings

Effective one-dimensional electric field coupling

Analytical form of the ground state

Significance of the simplified model

Abstract

We investigate the effects of the electromagnetic vacuum field on a harmonically bound electron. We show that in the electric-dipole approximation the model atom couples only to an effective one-dimensional electric field. In a simplified form, in which the problem is reduced to a single spatial dimension, we determine, analytically, the form of the ground state and discuss the significance of this.