A cold atom quantum simulator to explore pairing, condensation, and pseudogaps in extended Hubbard--Holstein models
We describe a quantum simulator for the Hubbard--Holstein model (HHM), comprising two dressed Rydberg atom species held in a monolayer by independent painted potentials, predicting that boson-mediated preformed pairing, and Berezinskii--Kosterlitz--Thouless (BKT) transition temperatures are experimentally accessible. The HHM is important for modeling the essential physics of unconventional superconductors. Experimentally realizable quantum simulators for HHMs are needed: (1) since HHMs are difficult to solve numerically and analytically, (2) to explore how competition between electron-phonon interactions and strong repulsion affects pairing in unconventional superconductors, (3) to understand the role of boson-mediated local pairing in pseudogaps and fermion condensates. We propose and study a quantum simulator for the HHM, using optical lattices, painted using zeros in the AC stark shift, to control two Rydberg atom species independently within a monolayer. We predict that interactions are sufficiently tunable to probe: (1) both HHMs and highly unconventional phonon-mediated repulsions, (2) the competition between intermediate-strength phonon and Coulomb mediated interactions, (3) BKT transitions, and preformed pairing that could be used to examine key hypotheses related to the pseudogap. We discuss how the quantum simulator can be used to investigate boson-mediated pairing and condensation of fermions in unconventional superconductors.