Collective P-Wave Orbital Dynamics of Ultracold Fermions

TL;DR

This paper explores the non-equilibrium orbital dynamics of ultracold fermions in optical lattices, deriving a model that reveals how collective behavior can be engineered via p-wave interactions and dispersion control.

Contribution

It introduces an extended Hubbard model for p-wave orbital interactions and demonstrates how dispersion engineering enables collective dynamics in ultracold fermions.

Findings

Dispersion engineering can suppress single-particle dispersion.

A collective many-body gap can be realized with moderate Feshbach tuning.

The Hamiltonian reduces to a Dicke model for orbital pseudo-spin.

Abstract

We consider the non-equilibrium 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 pseudo-spin. 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 pseudo-spin 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.