Three-body spin mixing in spin-1 Bose-Einstein condensates

TL;DR

This paper investigates three-body spin interactions in spin-1 Bose-Einstein condensates, revealing universal scattering behaviors and conditions where three-body effects dominate over two-body interactions.

Contribution

It provides a quantitative analysis of three-body scattering hypervolumes and their universal behavior, offering insights into spin mixing dynamics in spinor condensates.

Findings

Universal behavior of scattering hypervolumes for strong interactions

Three-body spin mixing can dominate at densities around 10^17 cm^-3

Tuning two-body interactions can suppress or enhance three-body effects

Abstract

We study zero-energy collisions between three identical bosons with spin $f = 1$ interacting via pairwise potentials. We quantify the corresponding three-body scattering hypervolumes, which parametrize the effective three-body interaction strengths in a many-body description of spin-1 Bose-Einstein condensates. Our results demonstrate universal behavior of the scattering hypervolumes for strong $s$- and $p$-wave two-body interactions. At weak interactions we find that the real parts of the scattering hypervolumes are predominantly determined by hard-hyperspherelike collisions which we characterize by a simple formula. With this universal result we estimate that spin mixing via three-body collisions starts to dominate over two-body spin mixing at a typical particle density of $10^{17}~\mathrm{cm}^{-3}$ for ${}^{23}$Na and ${}^{41}$K spinor condensates. This density can be reduced by tuning the two-body interactions to an $s$- or $p$-wave dimer resonance or to a point where two-body spin mixing effectively vanishes. Another possibility to observe effects of three-body spin mixing involves the application of weak magnetic fields to cancel out the effective two-body interaction strength in the characteristic timescale describing the spin dynamics.