Quantum knots in Bose-Einstein condensates created by counterdiabatic control

TL;DR

This paper presents a theoretical method using counterdiabatic control to create and precisely manipulate knotted structures with complex topologies in spin-1 Bose-Einstein condensates, confirmed by detailed simulations.

Contribution

It introduces an analytic approach for magnetic field evolution to generate and control quantum knots in BECs, enabling precise topological charge manipulation.

Findings

Successful creation of knots with Hopf charge > 1

Precise control over knot creation time and topology

Validation through 3D spin-1 Gross-Pitaevskii simulations

Abstract

We theoretically study the creation of knot structures in the polar phase of spin-1 BECs using the counterdiabatic protocol in an unusual fashion. We provide an analytic solution to the evolution of the external magnetic field that is used to imprint the knots. As confirmed by our simulations using the full three-dimensional spin-1 Gross-Pitaevskii equation, our method allows for the precise control of the Hopf charge as well as the creation time of the knots. The knots with Hopf charge exceeding unity display multiple nested Hopf links.