Measuring spatially extended density profiles using atom-cavity collective strong coupling to higher-order modes

Abstract

The collective strong coupling of rubidium atoms in a magneto-optical trap (MOT) to the Laguerre-Gaussian (LG) modes of a Fabry-P\'erot cavity is investigated. Bright and dark $^{85}\mathrm{Rb}$ MOT atoms are prepared at the geometric center of the cavity, and the vacuum Rabi splitting (VRS) of the collectively coupled atom-cavity system is measured for ${\mathrm{LG}}_{l0}$ ($l=0,1,2,3$) modes. The atom number coupled to the cavity mode depends on the overlap of the atomic density distribution and the specific spatial mode function, which is reflected in the measured VRS spectrum. The known mode function and the measured VRS can then be used to test whether the atomic density distribution in the experiment is Gaussian or uniform. A simple theoretical model for this process is described, and the experimental measurements are found to be in close agreement with the model.