Ultracold atoms in optical lattices provide an ideal set up for realizing some of the most pristine pseudogap states currently known from theoretical studies. Those states could be fundamentally different from the poorly understood pseudogap state of high-temperature superconductors, while exhibiting a similar phenomenology due to significant quantum fluctuations. This project focuses on the theoretical investigation of unconventional superfluid and insulating states of ultracold fermions in optical lattices. The idea is to identify and characterize those states in resonantly paired fermions and systematically explore the phase diagram of pair-density-wave and Fulde-Ferrell-Larkin-Ovchinnikov states in realistic lattice potentials. One of our main goals is to unveil the minimal microscopic ingredients required for the existence of those states so that they can be realized in experiments. The research will mostly rely on the unique combination of numerical methods that the two PIs have advanced in their recent work: exact diagonalization and quantum Monte Carlo simulations (M.R.), and order-parameter-dependent free energy minimization (P.N.).
This project will incorporate a broad outreach effort taking advantage of the location of George Mason and Georgetown Universities. Opportunities such as science fairs and public lectures will be used to attract high school and undergraduate students from Northern Virginia to pursue higher education and careers in science and engineering, as well as participate in the funded research projects. This grant will further facilitate the building of advanced research programs in atomic and condensed matter theory at George Mason and Georgetown Universities. Graduate students at both universities will receive training in high performance computing, and will gain experience performing highly parallel calculations in high performance computing centers within the US. We will encourage the participation of members of underrepresented groups in Physics and the results of this research will be reported in the joint conferences of the National Society of Black Physicists and the National Society of Hispanic Physicists.
