# Exact electrodynamics versus standard optics for a slab of cold dense gas

## TL;DR

This paper compares standard electrodynamics and atom-by-atom simulations for light propagation in cold dense gases, revealing qualitative differences when density and wavelength conditions lead to strong dipole-dipole interactions.

## Contribution

It demonstrates that mean-field electrodynamics may fail in dense gases where atom correlations become significant, highlighting the importance of microscopic simulations.

## Key findings

- Deviations from mean-field theory scale with $
ho k^{-3}$.
- Noticeable effects appear at $
ho k^{-3}
oughly 10^{-2}$.
- Simulations show shifts in resonance lines consistent with Lorentz-Lorenz and cooperative Lamb shifts.

## Abstract

We study light propagation through a slab of cold gas using both the standard electrodynamics of polarizable media, and massive atom-by-atom simulations of the electrodynamics. The main finding is that the predictions from the two methods may differ qualitatively when the density of the atomic sample $\rho$ and the wavenumber of resonant light $k$ satisfy $\rho k^{-3}\gtrsim 1$. The reason is that the standard electrodynamics is a mean-field theory, whereas for sufficiently strong light-mediated dipole-dipole interactions the atomic sample becomes correlated. The deviations from mean-field theory appear to scale with the parameter $\rho k^{-3}$, and we demonstrate noticeable effects already at $\rho k^{-3} \simeq 10^{-2}$. In dilute gases and in gases with an added inhomogeneous broadening the simulations show shifts of the resonance lines in qualitative agreement with the predicted Lorentz-Lorenz shift and "cooperative Lamb shift", but the quantitative agreement is unsatisfactory. Our interpretation is that the microscopic basis for the local-field corrections in electrodynamics is not fully understood.