Rydberg atom excitations in dense clouds alter the medium to be highly non-linear for single photon absorption, making possible all-optical quantum computing , single photon transistors , and single photon absorbers .However, in order to utilize Rydberg excitations in dense clouds for quantum optics, the rich physics and chemistry of Rydberg atoms interacting with a dense neutral-atom background gas, via low-energy electron-neutral and ion-neutral scattering, must be well understood.Collisions between the Rydberg electron and background neutral atoms, lead to a mean field density shift for Rydberg atoms, which is of the order 10MHz/ 10^14 cm^-3 for ^87 Rb triplet s-wave scattering.We exploit this density shift to characterize the mean density of our quantum gas, a Bose-Einstein Condensate (BEC), and to monitor the dynamics of the BEC phase transition, by analyzing the center of gravity of Rydberg spectra.We report how the mean field density shift, in combination with a density gradient, can also be used to localize Rydberg excitations in density shells with a spatial resolution less than optical wavelengths.This control of spatial excitation allows us to study the density-dependent quantum chemistry between a Rydberg atom and neutral atoms in a BEC.We discuss the implications of these results on experiments on charged impurities in quantum gases as well as wavefunction imaging based on electron-phonon coupling in a BEC.
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