The damping and diffusion of atoms moving in the background electromagnetic environment

TL;DR

This paper analyzes how atoms moving in a background electromagnetic field experience damping and diffusion forces, deriving general formulas and invariance properties that could help measure laboratory motion relative to radiation.

Contribution

It introduces a general approach to calculate damping and diffusion of atoms in electromagnetic backgrounds, applicable to multi-level atoms and invariant under Galilean transformations.

Findings

Center-of-mass motion is damped and diffused by electromagnetic interactions.

Formulas for damping force and diffusion coefficients are derived for multi-level atoms.

Results are invariant under Galilean transformations, enabling velocity measurements relative to background radiation.

Abstract

The interaction between an atom and the quantized electromagnetic field depends on the position of the atom. Then the atom experiences a force which is the minus gradient of this interaction. Through the Heisenberg equations of motion and the Born-Markov approximation, the mean and correlation of the force are obtained, showing that the center-of-mass motion of the atom is damped and diffused. This approach can be easily generalized to multi-level atoms, where the damping force and diffusion coefficients are just the weighted average of the contributions from all pairs of energy levels that have nonvanishing dipole elements. It is shown that these results are invariant under Galilean transformation, and in principle can be used to determine the velocity of the lab relative to the background radiation.