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Probe Knots and Hopf Insulators with Ultracold Atoms

TitleProbe Knots and Hopf Insulators with Ultracold Atoms
Publication TypeJournal Article
Year of Publication2018
AuthorsD-L. Deng, S-T. Wang, K. Sun, and L.. - M. Duan
JournalCHINESE PHYSICS LETTERS
Volume35
Pagination013701
Date PublishedJAN
Type of ArticleArticle
ISSN0256-307X
Abstract

Knots and links are fascinating and intricate topological objects. Their influence spans from DNA and molecular chemistry to vortices in superfluid helium, defects in liquid crystals and cosmic strings in the early universe. Here we find that knotted structures also exist in a peculiar class of three-dimensional topological insulators-the Hopf insulators. In particular, we demonstrate that the momentum-space spin textures of Hopf insulators are twisted in a nontrivial way, which implies the presence of various knot and link structures. We further illustrate that the knots and nontrivial spin textures can be probed via standard time-of-flight images in cold atoms as preimage contours of spin orientations in stereographic coordinates. The extracted Hopf invariants, knots, and links are validated to be robust to typical experimental imperfections. Our work establishes the existence of knotted structures in Hopf insulators, which may have potential applications in spintronics and quantum information processing.}, %%Address = {TEMPLE CIRCUS, TEMPLE WAY, BRISTOL BS1 6BE, ENGLAND

DOI10.1088/0256-307X/35/1/013701