Linked and knotted synthetic magnetic fields

TL;DR

This paper demonstrates how synthetic magnetic fields created through light-matter interactions in ultracold atoms can form linked and knotted configurations, with potential topological effects on Bose-Einstein condensates.

Contribution

It introduces a geometric framework for designing linked and knotted synthetic magnetic fields using Rabi frequency ratios in ultracold atomic systems.

Findings

Linked and knotted magnetic fields can be realized in ultracold atoms.

Synthetic gauge fields can induce topological vortex lines in BECs.

The geometric construction links field topology to Rabi frequency maps.

Abstract

We show that the realisation of synthetic magnetic fields via light-matter coupling in the Lambda-scheme implements a natural geometrical construction of magnetic fields, namely as the pullback of the area element of the sphere to Euclidean space via certain maps. For suitable maps, this construction generates linked and knotted magnetic fields, and the synthetic realisation amounts to the identification of the map with the ratio of two Rabi frequencies which represent the coupling of the internal energy levels of an ultracold atom. We consider examples of maps which can be physically realised in terms of Rabi frequencies and which lead to linked and knotted synthetic magnetic fields acting on the neutral atomic gas. We also show that the ground state of the Bose-Einstein condensate may inherit topological properties of the synthetic gauge field, with linked and knotted vortex lines appearing in some cases.