Rydberg molecule formation by a Rydberg atom in atomic Fermi superfluid

We consider a Rydberg atom immersed in a two-component atomic Fermi superfluid. The electron-atom scattering results in an attractive potential for the atoms in the superfluid to form a Rydberg molecule. The Fermi superfluid is formulated by the BCS-Leggett theory, and we solve the Bogoliubov-de Gennes (BdG) equation of the ground state with the Rydberg potential from first-principle calculations of selected Rydberg states. Analyzing the bound states from the BdG equation then identifies the formation of Rydberg molecules. On the BCS side with weak pairing interaction, the Rydberg potential typically breaks a Cooper pair and forms a Rydberg molecule between the Rydberg atom and a broken-pair fermion. On the BEC side, however, depending on the depth of the Rydberg potential, a Rydberg molecule between a Rydberg atom and a Cooper pair, or "pair in molecule", can emerge as a tightly bound Cooper pair falls into the Rydberg potential. The wavefunctions and energy spectrum from the BdG equation further demonstrate the rich physics behind Rydberg molecules in atomic Fermi superfluid.