We consider the nonequilibrium orbital dynamics of spin-polarized ultracold fermions in the first excited band of an optical lattice. A specific lattice depth and filling configuration is designed to allow the $p_x$ and $p_y$ excited orbital degrees of freedom to act as a pseudospin. Starting from the full Hamiltonian for $p$-wave interactions in a periodic potential, we derive an extended Hubbard-type model that describes the anisotropic lattice dynamics of the excited orbitals at low energy. We then show how dispersion engineering can provide a viable route to realizing collective behavior driven by $p$-wave interactions. In particular, Bragg dressing and lattice depth can reduce single-particle dispersion rates, such that a collective many-body gap is opened with only moderate Feshbach enhancement of $p$-wave interactions. Physical insight into the emergent gap-protected collective dynamics is gained by projecting the Hamiltonian into the Dicke manifold, yielding a one-axis twisting model for the orbital pseudospin that can be probed using conventional Ramsey-style interferometry. Experimentally realistic protocols to prepare and measure the many-body dynamics are discussed, including the effects of band relaxation, particle loss, spin-orbit coupling, and doping.

• Received 18 April 2021
• Revised 2 July 2021
• Accepted 25 August 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.143401