Quantum knots in Bose-Einstein condensates created by counterdiabatic control

T. Ollikainen, S. Masuda, M. Möttönen, M. Nakahara

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)
146 Downloads (Pure)


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.

Original languageEnglish
Article number063609
Pages (from-to)1-7
JournalPhysical Review A
Issue number6
Publication statusPublished - 7 Dec 2017
MoE publication typeA1 Journal article-refereed

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