Non-abelian Aharonov–Bohm experiment done at long last

01 Oct 2019

Phase shift: Images showing interference patterns (top) and a “Wilson loop” (bottom) were produced by the researchers to confirm the presence of non-Abelian gauge fields. (Courtesy: MIT)

For the first time, physicists in the US have confirmed a decades-old theory regarding the breaking of time-reversal symmetry in gauge fields. Marin Soljacic at the Massachusetts Institute of Technology and an international team of researchers have made this first demonstration of the “non-Abelian Aharonov–Bohm effect” in two optics experiments. With improvements, their techniques could find use in optoelectronics and fault-tolerant quantum computers.

First emerging in Maxwell’s famous equations for classical electrodynamics, a gauge theory is a description of the physics of fields. Gauge theories have since become an important part of physicists’ descriptions of the dynamics of elementary particles – notably the theory of quantum electrodynamics.

A salient feature of a gauge theory is that the physics it describes does not change when certain transformations are made to the underlying equations describing the system. An example is the addition of a constant scalar potential or a “curl-free” vector potential to Maxwell’s equations. Mathematically, this does not change the electric and magnetic fields that act on a charged particle such as an electron – and therefore the behaviour of the electron – so Maxwell’s theory is gauge invariant.

Just a phase

The Aharonov–Bohm effect arises in quantum mechanics because the addition of a potential results in the introduction of a phase in the wavefunction of the electron. Normally, this phase has no effect on the observed behaviour of the electron because the measurement of a property of the electron (such as its position) determines the amplitude of the wavefunction, not its phase.

However, this phase can be detected by measuring the quantum mechanical interference between electrons that have taken two different paths from a source to a detector. If these paths travel through regions with different local values of gauge potential, then a difference in phase will alter the interference pattern measured.

This effect was proposed in 1959 by Yakir Aharonov and David Bohm and confirmed by an experiment done by Robert Chambers in 1960. Chambers sent electrons on different paths that passed next to a very long solenoid. The magnetic field outside such a solenoid is negligible (and had little effect on the electron phase) but the vector potential outside a solenoid is significant and varies in space. As a result, electrons taking the different paths around the solenoid acquire different phases.

Rich in physics

This and subsequent observations of the effect involve “Abelian” systems, in which the physics plays out in the same way when time is run forwards and backwards. In 1975 Tai-Tsun Wu and Chen-Ning Yang conceived of the non-Abelian Aharonov–Bohm effect in which the gauge fields appear differently when time runs forwards or backwards. While expected to be rich in physics, the non-Abelian version of the effect has proved very difficult to achieve.

Now, Soljacic’s team has succeeded by creating two different types of non-Abelian gauge field using fibre-optic systems – with classical light waves taking the place of the electron wavefunction. They induced the first of these fields by passing light through a specialized crystal in a strong external magnetic field. The second non-Abelian gauge field was created by modulating the light using time-varying electrical signals

As hoped, they saw that both gauge fields produced two different interference patterns, depending on the direction of travel of the light. This showed that both gauge fields were indeed different when played forwards and backwards in time.

The team believes that the techniques developed for this first demonstration of the non-Abelian Aharonov–Bohm effect could lead to important technological and scientific advances in the future. “(This approach) might inspire the realization of exotic topological phases in quantum simulations using photons, polaritons, quantum gases, and superconducting qubits,” says Soljacic. “Combined with interactions, it may potentially one day serve as a platform for fault-tolerant topological quantum computation.”

The research is described in Science.

FROM PHYSICSWORLD.COM 6/10/2019