Rydberg-dressed atoms in BCS-state

We consider a system consisting of Rydberg dressed atoms interacting with BEC condensate of diatomic molecules. Using random phase approximation (RPA) we calculate the effective interactions between Rydberg atoms accounting for their Wan der Waals repulsion and exchange of virtual excitations of the condensate and demonstrate that total interaction can become attractive and BCS state of Rydberg dressed atoms can be formed. Using the example of 6Li atoms we demonstrate that the strength of the interactions can be controlled optically, and BCS regime is achievable at realistic experimental conditions.