Interactions of Rydberg atoms in a Bose-Einstein condensate*

Recent developments in ultracold Rydberg gases led to the prediction and discovery of ultra-long-range Rydberg molecules. A Rydberg atom can interact with a ground state atom and form a bound state, the so-called ``trilobite state,'' via an oscillatory Born-Oppenheimer potential arising from Rydberg electron-ground state atom low-energy scattering. Two Rydberg atoms can also be bound via a dispersion potential, and form a ``macrodimer.'' Here we consider two Rydberg atoms immersed in a dilute Bose-Einstein condensate (BEC). The interaction between the two Rydberg atoms is studied, and the formation of a possible ultra-long-range Rydberg molecule is shown.