Quantum knots in Bose-Einstein condensates created by counterdiabatic control

Abstract

We study theoretically the creation of knot structures in the polar phase of spin-1 Bose-Einstein condensates 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.

Knot Morphing Algorithm for Quantum `Fragile Topology'

“…The concept of knotted electromagnetic fields led to the first experimental images of topological three-dimensional skyrmions [13]. The timing of knot creation [20] and decay [19] are central to modeling quantum properties, as further explored here. Recent analysis of quantum manifolds [11] shares fundamental ideas with the surfaces presented here.…”

Counterdiabatic formalism of shortcuts to adiabaticity

“…Imperfect CD control is not always a bad thing. It is possible by taking advantage of this to create a topological link of the nematic vector bold-italicd of an oblate F=1 BEC in the polar phase [53]. The condition divbold-italicBCD=0 is imposed only along a ring in the condensate.…”

Counterdiabatic Formalism of Shortcuts to Adiabaticity

“…Imperfect CD control is not always a bad thing. It is possible by taking advantage of this to create a topological link of the nematic vector d of an oblate F = 1 BEC in the polar phase [53]. The condition divB CD = 0 is imposed only along a ring in the condensate.…”