Measuring Densities of Cold Atomic Clouds Smaller Than the Resolution Limit

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 in situ absorption images of elongated Sr-87 Fermi gases. We find significant nonlinear corrections to the estimated size and local density of the cloud compared to a standard analysis. This allows us to recover an undistorted 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.