Spin dynamics of Fermi gases in perturbed harmonic potentials

Spin-polarized fermions in a harmonic trap occupy evenly-spaced energy levels, and when inter-particle interactions are weak enough, these energy levels are equivalent to a lattice in energy space. Contact interactions between such trapped ultracold atoms in real space lead to a long-range interaction in lattice/energy space, and the many-body dynamics can be described by a Heisenberg lattice spin model. The parameters of this model can be tuned experimentally in ultracold gas experiments, and the non-equilibrium spin phases have previously been mapped out for a purely harmonic trap. A laser beam with tight focus can produce a localized perturbation to the harmonic potential, altering the energy levels and wave functions occupied by the fermions. We explore the effects of such localized perturbations on the interactions between pairs of particles in the trap, and work towards predicting the perturbation's effect on the many-body spin dynamics in the Heisenberg model, as well as potential experimental signatures.