The two-atom energy spectrum in a harmonic trap near a Feshbach resonance at higher partial waves

TL;DR

This paper derives and verifies the universal energy spectrum for two atoms in a harmonic trap near a higher partial wave Feshbach resonance, extending previous p-wave results and exploring the spectrum's limitations.

Contribution

It provides a universal $l=2$ energy spectrum for two atoms near a higher partial wave Feshbach resonance, extending prior p-wave work and analyzing its applicability.

Findings

Derived the $l=2$ energy spectrum near Feshbach resonance.

Validated the spectrum with numerical Schrödinger equation solutions.

Explored the limitations of the universal spectrum for higher partial waves.

Abstract

Two atoms in an optical lattice may be made to interact strongly at higher partial waves near a Feshbach resonance. These atoms, under appropriate constraints, could be bosonic or fermionic. The universal $l=2$ energy spectrum for such a system, with a caveat, is presented in this paper, and checked with the spectrum obtained by direct numerical integration of the Schr\"odinger equation. The results reported here extend those of Yip for p-wave resonance (Phys. Rev. A {\bf 78}, 013612 (2008)), while exploring the limitations of a universal expression for the spectrum for the higher partial waves.