Braiding with Borromean Rings in (3+1)-Dimensional Spacetime

Understand

While winding a particle-like excitation around a loop-like excitation yields the celebrated Aharonov-Bohm phase, we find a distinctive braiding phase in the absence of such mutual winding.

• In this work, we propose an exotic particle-loop-loop braiding process, dubbed the \emph{Borromean-Rings braiding}.
• In the process, a particle moves around two unlinked loops, such that its trajectory and the two loops form the Borromean-Rings or more general Brunnian links.
• As the particle trajectory does not wind with any of the loops, the resulting braiding phase is fundamentally different from the Aharonov-Bohm phase.