Strongly interacting fermions in optical lattices: from few to many particles

J. P. Kestner, Luming Duan

Ariel Sommer, Lawrence W. Cheuk, Mark Ku +3 more

Ehsan Khatami, Marcos Rigol

Michael L. Wall, Lincoln D. Carr

We numerically study the problem of two fermions in a three-dimensional optical lattice interacting via a zero-range Feshbach resonance and display the dispersions of the bound states as a two-particle band structure with unique features compared to typical single-particle band structures. We show that the exact two-particle solutions of a projected Hamiltonian may be used to define an effective two-channel, few-band model for the low-energy, low-density physics of many fermions at arbitrary s-wave scattering length. Our method applies to resonances of any width and can be adapted to multichannel situations or higher-ℓ pairing. In strong contrast to usual Hubbard physics, we find that pair hopping is significantly altered by strong interactions and the presence of the lattice, and the lattice induces multiple molecular bound states.

Tilman Esslinger

Zhihao Xu, Shu Chen

We demonstrate that the static structure factor, momentum distribution, and density distribution provide clear signatures of the emergence of Wigner crystal for the fermionic dipolar gas with strongly repulsive dipole-dipole interactions trapped in one-dimensional optical lattices. Our numerical evidences are based on the exact diagonalization of the microscopic effective lattice Hamiltonian of few particles interacting with long-range interactions. As a comparison, we also study the system with only nearest-neighbor interactions, which displays quite different behavior from the dipolar system in the regime of strong repulsion.