Numerical Study of the stability of Skyrmions in Bose-Einstein Condensates

TL;DR

This paper investigates the stability of three-dimensional Skyrmions in trapped Bose-Einstein condensates, highlighting the influence of physical parameters and proposing stabilization methods.

Contribution

It provides a detailed numerical analysis of how scattering lengths, atom numbers, and trap parameters affect Skyrmion stability in BECs, including stabilization techniques.

Findings

Stability depends critically on scattering lengths, atom numbers, and trap geometry.

Stable Skyrmions can exist with as few as 2 million atoms in cigar-shaped traps.

Laser pinning can prevent Skyrmions from drifting out of the trap.

Abstract

We show that the stability of three-dimensional Skyrmions in trapped Bose-Einstein condensates depends critically on scattering lengths, atom numbers, trap rotation and trap anisotropy. In particular, for the $^{87}$Rb $|F=1,m_{f}=-1>$, $|F=2,m_{f}=1>$ hyperfine states stability is sensitive to the scattering lengths at the level of their present experimental uncertainties. In a cigar shaped trap, we find stable Skyrmions with as few as $2\times10^{6}$ atoms, a number which scales with the inverse square root of the trap frequency. These can be stabilized against drift out of the trap by laser pinning.