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Non-Abelian Gauge Fields Directly Observed for First Time

After decades of unsuccessful attempts, physicists have directly observed an exotic physical phenomenon called the non-Abelian Aharonov-Bohm effect. The findings could lead to realizations of what are known as topological phases, and eventually to advances toward fault-tolerant quantum computers.

To confirm the presence of non-Abelian gauge fields, Yang et al produced interference patterns (top) and a Wilson loop (bottom). Image credit: Yang et al, doi: 10.1126/science.aay3183.

To confirm the presence of non-Abelian gauge fields, Yang et al produced interference patterns (top) and a Wilson loop (bottom). Image credit: Yang et al, doi: 10.1126/science.aay3183.

Gauge fields, which describe transformations that particles undergo, are crucial for understanding and manipulation of physical systems.

These fields fall into two classes: Abelian, in which the measured effects on an observable parameter are commutative; and non-Abelian, where the sequence in which the field is applied matters.

The Aharonov-Bohm effect, named after the theorists who predicted it in 1959, confirmed that gauge fields have physical consequences. But the observations only worked in Abelian systems.

In 1975, Tai-Tsun Wu and Chen-Ning Yang generalized the effect to the non-Abelian regime as a thought experiment. Nevertheless, it remained unclear whether it would even be possible to ever observe the effect in a non-Abelian system.

Physicists lacked ways of creating the effect in the lab, and also lacked ways of detecting the effect even if it could be produced.

Now, both of those puzzles have been solved, and the observations carried out successfully.

“Virtually all fundamental physical phenomena are time-invariant. That means that the details of the way particles and forces interact can run either forward or backward in time, and a movie of how the events unfold can be run in either direction, so there’s no way to tell which is the real version,” explained MIT graduate student Yi Yang, University of Pennsylvania’s Professor Bo Zhen and their colleagues.

“Creating the Abelian version of the Aharonov-Bohm effects requires breaking the time-reversal symmetry, a challenging task in itself,” added MIT Professor Marin Soljacic.

“But to achieve the non-Abelian version of the effect requires breaking this time-reversal multiple times, and in different ways, making it an even greater challenge.”

To produce the effect, the physicists use photon polarization. Then, they produced two different kinds of time-reversal breaking.

They used fiber optics to produce two types of gauge fields that affected the geometric phases of the optical waves, first by sending them through a crystal biased by powerful magnetic fields, and second by modulating them with time-varying electrical signals, both of which break the time-reversal symmetry.

They were then able to produce interference patterns that revealed the differences in how the light was affected when sent through the fiber-optic system in opposite directions, clockwise or counterclockwise.

Without the breaking of time-reversal invariance, the beams should have been identical, but instead, their interference patterns revealed specific sets of differences as predicted, demonstrating the details of the elusive effect.

“The original, Abelian version of the Aharonov-Bohm effect has been observed with a series of experimental efforts, but the non-Abelian effect has not been observed until now,” Yang said.

“The finding allows us to do many things, opening the door to a wide variety of potential experiments, including classical and quantum physical regimes, to explore variations of the effect.”

The results appear in the journal Science.


Yi Yang et al. 2019. Synthesis and observation of non-Abelian gauge fields in real space. Science 365 (6457): 1021-1025; doi: 10.1126/science.aay3183

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