Three-Body Problem of Bosons nearby a d-wave Resonance

TL;DR

This paper explores the unique three-body interactions and recombination rates of spinless bosons near a d-wave resonance, revealing behaviors distinct from s-wave resonances and mean-field predictions.

Contribution

It provides the first detailed calculation of atom-dimer scattering length and three-body recombination rates for bosons near a d-wave resonance using STM equations.

Findings

Atom-dimer scattering length is positive and smaller than mean-field estimate.

Recombination rate is nearly constant on the quasi-bound side.

Recombination rate increases monotonically across the unitarity point.

Abstract

Motivated by recent experimental progresses, we investigate few-body properties of interacting spinless bosons nearby a d-wave resonance. Using the Skorniakov-Ter-Martirosion (STM) equations, we calculate the scattering length between an atom and a d-wave dimer, and we find that the atom-dimer scattering length is positive and is much smaller the result from the mean-field approximation. We also reveal unique properties of the three-body recombination rate for a degenerate Bose condensate nearby the d-wave resonance. We find that the total recombination rate is nearly a constant at the quasi-bound side, in contrast to the behavior of a thermal gas nearby high-partial wave resonance. We also find that the recombination rate monotonically increases across the unitary point toward the bound side, which is due to the largely enhanced coupling between the atom and the d-wave dimer with deeper binding energy. This monotonic behavior is also qualitatively different from that of a degenerate gas nearby an s-wave resonance counterpart.