nLab described the Yang monopole in a mathematical way. In short, we could view Yang monopole as the generalization of the Dirac monopole from 3+1 dimensional spacetime to 5+1 dimensional spacetime.

Comparison to Dirac monopole

The Dirac monopole lives in 3D space and has a non-trivial first Chern number. The Yang monopoles lives in 5D space and has a non-trivial second Chern number with zero first Chern number. The Dirac monopole deals with U(1) gauge fields (scalar) whereas Yang monopole deals with non-abelian SU(2) gauge fields (matrix). Under U(1) gauge fields, the Berry phase is a scalar, if you adiabatically traverse a state along a closed loop, one could obtain an additional U(1) phase. Under SU(2) gauge fields, the Berry phase is a matrix, a spin up could become a spin down after the same process.

U(1) gauge field vs SU(2) gauge field

Synthetic dimension

Even though a magnetic monopole (or Dirac monopole) does not exist in nature. One could still engineer a 3D synthetic magnetic field and simulate a Dirac monopole. A Yang Monopole lives in 5D. We have to use synthetic dimension. Here, one could use 5D parameter space. That is, 5 dimensions consist of laser intensities, phases, and detuning. We often use coupled two state model to describe a spin half on a Bloch sphere (equivalent to a Dirac monopole in the origin). One need a S4 Bloch sphere to enclose a Yang monopole. That is, one need a spin 3/2 or four states. Sugawa et. al., Science 360, 1429 (2018) simulated a Yang monopole by cyclically couple 4 internal states of a spinor BEC.

Compare Dirac with Yang Monopole in Experiment

Effect of interaction

Atoms weakly interact, we would like to investigate how and if interaction changes the physical picture. When the interaction is weak, the non-interaction picture works well. But when the interaction is strong, we found that Yang monopole could split or high dimensional topological defects other than point defect could arise.