Tunable pairing with local spin-dependent Rydberg molecule potentials in an atomic Fermi superfluid

We explore the energy spectrum and eigenstates of two-component atomic Fermi superfluids with tunable pairing interactions in the presence of spin-dependent ultralong-range Rydberg molecule (ULRM) potentials, within the Bogoliubov–de Gennes formalism. The attractive ULRM potentials lead to local-density accumulation, while their difference results in a local polarization potential and induces the in-gap Yu-Shiba-Rusinov (YSR) states whose energies lie below the bulk energy gap. A transition from equal population to population imbalance occurs as the pairing strength falls below a critical value, accompanied by the emergence of local Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)–like states characterized by out-of-phase wave functions and lower energies compared to the YSR states. The negative contribution emanating from the FFLO-like states also causes a sign change in the gap function within the ULRM potentials. Depending on the Rydberg excitation, the transition towards population imbalance can be on either the BCS or the Bose-Einstein condensation side of the Fermi superfluid. Additionally, spin-polarized bound states arise along with oscillatory “clumpy states” to compensate for the local-density difference. Here, we discuss possible experimental realizations of the composite Rydberg-atom–Fermi-superfluid system.. Authors: Chien, Chih-Chun [University of California, Merced, CA (United States)] (ORCID:0000000311611846); Rittenhouse, Seth T. [United States Naval Academy, Annapolis, MD (United States); Harvard & Smithsonian, Cambridge, MA (United States)] (ORCID:0000000216877320); Mistakidis, S. I. [Harvard & Smithsonian, Cambridge, MA (United States); Missouri University of Science and Technology, Rolla, MO (United States)] (ORCID:0000000251185792); Sadeghpour, H. R. [Harvard & Smithsonian, Cambridge, MA (United States)] (ORCID:0000000157078675). DOE Contract: SC0025809. Subjects: Cold and ultracold molecules; Fermionic condensates; Rydberg gases