Rydberg Electrons in a Bose-Einstein Condensate

We investigate a hybrid system composed of ultracold Rydberg atoms immersed in an atomic Bose-Einstein condensate (BEC). The coupling between the Rydberg electrons and BEC atoms leads to the excitation of phonons, the exchange of which induces Yukawa interaction between Rydberg atoms. Due to the small electron mass, the effective charge associated with this quasi-particle-mediated interaction can be large, while its range is equal to the healing length of the BEC, which can be tuned by adjusting the scattering length of the BEC atoms. We find that for small healing lengths, the distortion of the BEC can "image" the wave function density of the Rydberg electron, while large healing lengths induce an attractive Yukawa potential between the two Rydberg atoms that can form a new type of ultra-long-range molecule. We discuss both cases for a realistic system.