Analytical solutions for two atoms in a harmonic trap: p-wave interactions

TL;DR

This paper derives analytical solutions for two ultracold fermions in a harmonic trap with p-wave interactions, incorporating energy-dependent scattering and resonances, validated against model potentials and applied to Feshbach resonances.

Contribution

It introduces an analytical framework for p-wave interactions in trapped ultracold atoms using pseudopotentials and quantum-defect theory, extending understanding near Feshbach resonances.

Findings

Excellent agreement with model potential energy levels

Derived simple formulas for energy-dependent scattering volume

Analyzed energy spectrum near p-wave Feshbach resonance

Abstract

We derive analytical solutions for the system of two ultracold spin-polarized fermions interacting in p wave and confined in an axially symmetric harmonic trap. To this end we utilize p-wave pseudopotential with an energy-dependent scattering volume. This allows to describe the scattering in tight trapping potentials in the presence of scattering resonances. We verify predictions of the pseudopotential treatment for some model interaction potential, obtaining an excellent agreement with exact energy levels. Then we turn to the experimentally relevant case of neutral atom interactions in the vicinity of a p-wave Feshbach resonance. In the framework of the multichannel quantum-defect theory we derive relatively simple formula for an energy-dependent scattering volume, and later we apply it to investigate the energy spectrum of trapped atoms close to the p-wave Feshbach resonance.