On the Dipole Approximation with Error Estimates

TL;DR

This paper rigorously justifies the dipole approximation for atom-radiation interactions by proving convergence in the limit of infinite wavelength and providing error estimates, including for realistic fields.

Contribution

It provides a mathematical proof of the dipole approximation's validity and error bounds, extending to N-body Coulomb systems and common electromagnetic fields.

Findings

Proves the dipole approximation in the infinite wavelength limit.

Estimates the rate of convergence for the approximation.

Includes realistic electromagnetic field models like plane waves and laser pulses.

Abstract

The dipole approximation is employed to describe interactions between atoms and radiation. It essentially consists of neglecting the spatial variation of the external field over the atom. Heuristically, this is justified by arguing that the wavelength is considerably larger than the atomic length scale, which holds under usual experimental conditions. We prove the dipole approximation in the limit of infinite wavelengths compared to the atomic length scale and estimate the rate of convergence. Our results include N-body Coulomb potentials and experimentally relevant electromagnetic fields such as plane waves and laser pulses.