Many-body theories of density response for a strongly correlated Fermi gas

Recent breakthroughs in the creation of ultra-cold atomic gases in the laboratory have ushered in major changes in physical science. Many novel experiments are now possible, with an unprecedented control of interaction, geometry and purity. Quantum many-body theory is facing severe challenges in quantitatively understanding new experimental results. Here, we review some recently developed theoretical techniques that provide successful predictions for density response of a strongly correlated atomic Fermi gas. These include the strong-coupling random-phase approximation theory, high-temperature quantum virial expansion, and asymptotically exact Tan relations applicable at large momentum.