@article { WOS:000702389700001,
title = {Wilson loop and Wilczek-Zee phase from a non-Abelian gauge field},
journal = {npj Quantum Inform.},
volume = {7},
number = {1},
year = {2021},
month = {SEP 30},
publisher = {NATURE PORTFOLIO},
type = {Article},
abstract = {Quantum states can acquire a geometric phase called the Berry phase after adiabatically traversing a closed loop, which depends on the path not the rate of motion. The Berry phase is analogous to the Aharonov-Bohm phase derived from the electromagnetic vector potential, and can be expressed in terms of an Abelian gauge potential called the Berry connection. Wilczek and Zee extended this concept to include non-Abelian phases-characterized by the gauge-independent Wilson loop-resulting from non-Abelian gauge potentials. Using an atomic Bose-Einstein condensate, we quantum-engineered a non-Abelian SU(2) gauge field, generated by a Yang monopole located at the origin of a 5-dimensional parameter space. By slowly encircling the monopole, we characterized the Wilczek-Zee phase in terms of the Wilson loop, that depended on the solid-angle subtended by the encircling path: a generalization of Stokes{\textquoteright} theorem. This observation marks the observation of the Wilson loop resulting from a non-Abelian point source.},
doi = {10.1038/s41534-021-00483-2},
author = {Sugawa, Seiji and Salces-Carcoba, Francisco and Yue, Yuchen and Putra, Andika and Spielman, I. B.}
}
@article {10056,
title = {Second Chern number of a quantum-simulated non-Abelian Yang monopole},
journal = {Science},
volume = {360},
year = {2018},
pages = {1429{\textendash}1434},
abstract = {Topological properties of physical systems are reflected in so-called Chern numbers: A nonzero Chern number typically means that a system is topologically nontrivial. Sugawa et al. engineered a cold atom system with a nonzero second Chern number, in contrast to condensed matter physics, where only the first Chern number is usually invoked. The exotic topology relates to the emergence of a type of magnetic monopole called the Yang monopole (known from theoretical high-energy physics) in a five-dimensional space of internal degrees of freedom in a rubidium Bose-Einstein condensate. The results illustrate the potential of cold atoms physics to simulate high-energy phenomena.Science, this issue p. 1429Topological order is often quantified in terms of Chern numbers, each of which classifies a topological singularity. Here, inspired by concepts from high-energy physics, we use quantum simulation based on the spin degrees of freedom of atomic Bose-Einstein condensates to characterize a singularity present in five-dimensional non-Abelian gauge theories{\textemdash}a Yang monopole. We quantify the monopole in terms of Chern numbers measured on enclosing manifolds: Whereas the well-known first Chern number vanishes, the second Chern number does not. By displacing the manifold, we induce and observe a topological transition, where the topology of the manifold changes to a trivial state.

},
issn = {0036-8075},
doi = {10.1126/science.aam9031},
url = {http://science.sciencemag.org/content/360/6396/1429},
author = {Sugawa, Seiji and Salces-Carcoba, Francisco and Perry, Abigail R. and Yue, Yuchen and Ian B Spielman}
}