Tying Quantum Knots

TL;DR

This paper reports the first experimental creation and detection of topologically non-trivial knot solitons in a quantum Bose-Einstein condensate, linking classical knot concepts with quantum matter.

Contribution

It demonstrates controlled generation and imaging of quantum knot solitons, establishing a foundation for future quantum topological studies.

Findings

First experimental observation of quantum knot solitons.

Images reveal the Hopf fibration structure in a quantum system.

Establishes a link between classical knots and quantum topological textures.

Abstract

Knots are familiar entities that appear at a captivating nexus of art, technology, mathematics, and science. As topologically stable objects within field theories, they have been speculatively proposed as explanations for diverse persistent phenomena, from atoms and molecules to ball lightning and cosmic textures in the universe. Recent experiments have observed knots in a variety of classical contexts, including nematic liquid crystals, DNA, optical beams, and water. However, no experimental observations of knots have yet been reported in quantum matter. We demonstrate here the controlled creation and detection of knot solitons in the order parameter of a spinor Bose-Einstein condensate. The experimentally obtained images of the superfluid directly reveal the circular shape of the soliton core and its accompanying linked rings. Importantly, the observed texture corresponds to a topologically non-trivial element of the third homotopy group and demonstrates the celebrated Hopf fibration, which unites many seemingly unrelated physical contexts. Our observations of the knot soliton establish an experimental foundation for future studies of their stability and dynamics within quantum systems.