Bound states and Cooper pairs of molecules in 2D optical lattices bilayer

Abstract

We investigate the formation of Cooper pairs, bound dimers and the dimer-dimer elastic scattering of ultracold dipolar Fermi molecules confined in a 2D optical lattice bilayer configuration. While the energy and their associated bound states are determined in a variational way, the correlated two-molecule pair is addressed as in the original Cooper formulation. We demonstrate that the 2D lattice confinement favors the formation of zero center mass momentum bound states. Regarding the Cooper pairs binding energy, this depends on the molecule populations in each layer. Maximum binding energies occur for non-zero (zero) pair momentum when the Fermi system is polarized (unpolarized). We find an analytic expression for the dimer-dimer effective interaction in the deep BEC regime. The present analysis represents a route for addressing the BCS-BEC crossover in dipolar Fermi gases confined in 2D optical lattices within the current experimental panorama.

Lattice polaron in a Bose–Einstein condensate of hard-core bosons

“…Then, we would expect the energy of the polaron to lie below the energy of the bound state. Confined to optical lattices, the study of the scattering between a pair of atoms from a two-body perspective [90][91][92] has predicted the emergence of both long-lived attractive and repulsive bound states, which were experimentally observed [93].…”

p‐Wave Superfluid Phases of Fermi Molecules in a Bilayer Lattice Array

“…First, we investigate the bound energies as a function of χ. In Figure we plot the solutions for the binding energy given by the following equation: where is the Fourier transform of the interaction potential, , with q the relative momentum between two molecules lying in layers A and B , and Ω the number of sites. , where is the center of mass vector in the first Brillouin zone.…”