Probing a quantum gas with single Rydberg atoms

We present a novel spectroscopic method for probing the insitu~density of quantum gases. We exploit the density-dependent energy shift of highly excited {Rydberg} states, which is of the order $10$MHz,/,1E14,cm$^{text{-3}}$ for rubidium~for triplet s-wave scattering. The energy shift combined with a density gradient can be used to localize Rydberg atoms in density shells with a spatial resolution less than optical wavelengths, as demonstrated by scanning the excitation laser spatially across the density distribution. We use this Rydberg spectroscopy to measure the mean density addressed by the Rydberg excitation lasers, and to monitor the phase transition from a thermal gas to a Bose-Einstein condensate (BEC).