Probing p-wave interactions with orbital degrees of freedom in optical lattice systems

We present a protocol for engineering and observing the many-body dynamics of spin-polarized ultracold fermions interacting via p-wave collisions and loaded in an optical lattice with motion along two dimensions. Our scheme requires a filling of two atoms per site, one in the ground band and another in the subspace of two low-lying excited orbital states. The filled ground band prevents relaxation from the excited bands via Pauli exclusion. A Bragg-type laser coupling is used to dress the orbital states, making their single-particle dispersion highly isotropic. The reduced differential kinetic energy of the dressed states enables p-wave interactions to act collectively and dominate at realistic timescales with a moderate Feshbach enhancement of the scattering volume. In an appropriate parameter regime, we show that the many-body dynamics can be accurately described by a spin model acting on the excited orbitals, and further reduced to a one-axis twisting (OAT) model. We discuss experimentally accessible interferometric protocols to probe the collective OAT dynamics in the orbital degrees of freedom as well as methods of state preparation and measurement using ultracold alkali 40K atoms.