A Computational Study of Dynamical Properties of Cold Atomic Fermi Systems: Trapped Gases and Systems Moving on Optical Lattices

We present preliminary results of a study of a cold atomic Fermi gas in a few relevant density regimes, addressing trapped dilute gases and gases embedded in optical lattices, modeled with a Hubbard Model Hamiltonian. This work builds on our previous research on the supersolid phase, which arises in a two-dimensional Fermi gas at half-filling, spin-balanced, on an optical lattice. Researchers in many areas of physics are interested in cold atoms because of their potential to serve as physical models of seemingly unrelated systems, such as superconductors and the superfluid interiors of neutron stars. Leveraging quantum Monte Carlo (QMC) simulations and cutting-edge analytic continuation techniques we can obtain unbiased results for static and dynamical correlation functions. We also apply Generalized Random Phase Approximation (GRPA) in our investigation. QMC, unlike GRPA, gives exact results. However, GRPA allows for much finer resolution in the momentum domain when calculating dynamical correlation functions. Consequently, the strengths of one method make up for the potential weaknesses in the other. Taken together, these methodologies provide an excellent set of tools for studying the exotic and counterintuitive properties of cold atomic gases.