Stable knots in the trapped Bose-Einstein condensates

TL;DR

This paper investigates stable knotted spin textures in two-component Bose-Einstein condensates, demonstrating their topological properties and stability through exact solutions and numerical simulations of the Gross-Pitaevskii equations.

Contribution

It presents the first exact solution of a topologically non-trivial knot in trapped Bose-Einstein condensates and verifies its stability numerically.

Findings

Identified a non-trivial topological knot with Hopf invariant in BECs.

Demonstrated stability of the knot via imaginary time evolution.

Provided an exact solution within the non-interacting regime.

Abstract

The knot of spin texture is studied within the two-component Bose-Einstein condensates which are described by the nonlinear Gross-Pitaevskii equations. We start from the non-interacting equations including an axisymmetric harmonic trap to obtain an exact solution, which exhibits a non-trivial topological structure. The spin-texture is a knot with an integral Hopf invariant. The stability of the knot is verified by numerically evolving the nonlinear Gross-Pitaevskii equations along imaginary time.