Synthetic Topological Vacua of Yang-Mills Fields in Bose-Einstein Condensates

TL;DR

This paper proposes and demonstrates a method to create and observe synthetic topological vacua in Bose-Einstein condensates, enabling experimental exploration of complex quantum field topologies.

Contribution

It introduces a novel experimental platform for simulating and studying topological vacua of Yang-Mills fields using Bose-Einstein condensates.

Findings

Successfully synthesized vacuum with topological number n=1 and measured Hopf index.

Realized vacuum with topological number n=2 showing distinctive spin textures.

Demonstrated that different topological vacua have unique spatial structures.

Abstract

Topological vacua are a family of degenerate ground states of Yang-Mills fields with zero field strength but nontrivial topological structures. They play a fundamental role in particle physics and quantum field theory, but have not yet been experimentally observed. Here we report the first theoretical proposal and experimental realization of synthetic topological vacua with a cloud of atomic Bose-Einstein condensates. Our setup provides a promising platform to demonstrate the fundamental concept that a vacuum, rather than being empty, has rich spatial structures. The Hamiltonian for the vacuum of topological number n = 1 is synthesized and the related Hopf index is measured. The vacuum of topological number n = 2 is also realized, and we find that vacua with different topological numbers have distinctive spin textures and Hopf links. Our work opens up opportunities for exploring topological vacua and related long-sought-after instantons in tabletop experiments.