Tailoring Bose-Einstein-condensate environments for a Rydberg impurity

Abstract

Experiments have demonstrated that the excitation of atoms embedded in a Bose-Einstein condensate to Rydberg states is accompanied by phonon creation. Here we provide the theoretical basis for the description of phonon-induced decoherence of the superposition of two different Rydberg states. To this end, we determine Rydberg-phonon coupling coefficients using a combination of analytical and numerical techniques. From these coefficients, we calculate bath correlation functions, spectral densities, and reorganization energies. These quantities characterize the influence of the environment and form essential inputs for followup open quantum system approaches. We find that the amplitude of bath correlations scales like the power law ${\ensuremath{\nu}}^{\ensuremath{-}6}$ with the principal quantum number $\ensuremath{\nu}$, while reorganization energies scale exponentially, reflecting the extreme tunability of Rydberg atomic properties.