Probe knots and Hopf insulators with ultracold atoms 1 DONG
Ling Deng, Sheng-Tao Wang, Kai Sun, L.-M. Duan · 2015
strings in the early universe. Here, we show that knotted structures also exist in a peculiar class of three dimensional topological insulators|the Hopf insulators. In particular, we demonstrate that the spin textures of Hopf insulators in momentum space are twisted in a nontrivial way, which implies various knot and link structures. We further illustrate that the knots and nontrivial spin textures can be probed via standard time-of-ight 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 cold atoms and may have potential applications in spintronics and quantum information processings.