Resonant Feshbach scattering of fermions in one-dimensional optical lattices

TL;DR

This paper develops a scattering theory for fermions in a 1D optical lattice, showing how lattice symmetry allows tuning Feshbach resonances via center-of-mass momentum within a single band approximation.

Contribution

It introduces a novel formulation of Feshbach scattering in a lattice setting, exploiting symmetry and band structure to control resonance positions.

Findings

Resonance position depends on center-of-mass momentum.

Lattice symmetry enables factorization of the scattering problem.

Single band approximation simplifies the analysis.

Abstract

We consider Feshbach scattering of fermions in a one-dimensional optical lattice. By formulating the scattering theory in the crystal momentum basis, one can exploit the lattice symmetry and factorize the scattering problem in terms of center-of-mass and relative momentum in the reduced Brillouin zone scheme. Within a single band approximation, we can tune the position of a Feshbach resonance with the center-of-mass momentum due to the non-parabolic form of the energy band.