Topological Objects in Two-component Bose-Einstein Condensates

TL;DR

This paper compares two theories of two-component Bose-Einstein condensates, revealing they produce similar topological objects and identifying a Skyrme-like gauge theory that admits complex vortex and knot solutions.

Contribution

It demonstrates the equivalence of topological objects in Gross-Pitaevskii and gauge theories, and constructs the lightest knot solution numerically.

Findings

Both theories produce similar topological objects.

The gauge theory is similar to Skyrme theory, admitting non-Abelian vortices and knots.

Constructed the lightest knot solution numerically.

Abstract

We study the topological objects in two-component Bose-Einstein condensates. We compare two competing theories of two-component Bose-Einstein condensate, the popular Gross-Pitaevskii theory and the recently proposed gauge theory of two-component Bose-Einstein condensate which has an induced vorticity interaction. We show that two theories produce very similar topological objects, in spite of the obvious differences in dynamics. Furthermore we show that the gauge theory of two-component Bose-Einstein condensate, with the U(1) gauge symmetry, is remarkably similar to the Skyrme theory. Just like the Skyrme theory the theory admits the non-Abelian vortex, the helical vortex, and the vorticity knot. We construct the lightest knot solution in two-component Bose-Einstein condensate numerically, and discuss how the knot can be constructed in the spin-1/2 condensate of $^{87}{\rm Rb}$ atoms.