Measuring densities of cold atomic clouds smaller than the resolution limit

TL;DR

This paper introduces a novel absorption imaging technique to measure the size and density of atomic clouds smaller than the imaging resolution by leveraging optical thickness and shape assumptions.

Contribution

The authors develop and experimentally validate a method to accurately determine sub-resolution cloud dimensions and densities using absorption imaging with non-linear corrections.

Findings

Successfully measured transverse sizes as small as one quarter of the resolution.

Found significant non-linear corrections improve size and density estimates.

Demonstrated method on elongated 87Sr Fermi gases.

Abstract

We propose and demonstrate an experimental method to measure by absorption imaging the size and local column density of a cloud of atoms, even when its smallest dimension is smaller than the resolution of the imaging system. To do this, we take advantage of the fact that, for a given total number of atoms, a smaller and denser cloud scatters less photons when the gas is optically thick. The method relies on making an ansatz on the cloud shape along the unresolved dimension(s), and on providing an additional information such as the total number of atoms. We demonstrate the method on \textit{in-situ} absorption images of elongated 87Sr Fermi gases. We find significant non-linear corrections to the estimated size and local density of the cloud compared to a standard analysis. This allows us to recover an un-distorted longitudinal density profile, and to measure transverse sizes as small as one fourth of our imaging resolution. The ultimate limit of our method is the wavelength that is used for imaging.