Non-Abelian Gauge Field Mechanics

Abstract:Non-Abelian gauge fields play a key role in describing the behavior of particles whose motion is coupled to internal degrees of freedom, such as their spin. Here, we experimentally realize a tuneable non-Abelian gauge field in an active mechanical lattice by using pairs of oscillators to encode a local pseudo-spin for each site, with inter-site spin-dependent couplings engineered via real-time measurement and feedback. We experimentally extract Wilson-loop observables in our set-up and hence demonstrate that we can create a genuinely non-Abelian gauge field. We then exploit the controllability of our mechanical lattice to engineer non-reciprocal hoppings to explore non-Hermitian non-Abelian gauge potentials. For a two-dimensional (2D) lattice, we demonstrate that the non-Hermiticity can manifest in direction-dependent Wilson loops for a single plaquette, while for a one-dimensional (1D) system, we show that a non-Abelian gauge potential can switch the localization of non-Hermitian skin modes between opposite ends of a chain. Our work establishes active mechanical lattices as a flexible and programmable platform for probing non-Abelian gauge fields and exploring their interplay with non-Hermitian dynamics.

Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Other Condensed Matter (cond-mat.other); Classical Physics (physics.class-ph); Quantum Physics (quant-ph)

arXiv:2607.18215 [cond-mat.mes-hall]

(or arXiv:2607.18215v1 [cond-mat.mes-hall] for this version)

https://doi.org/10.48550/arXiv.2607.18215 arXiv-issued DOI via DataCite (pending registration)