Spin-orbit coupling in a hexagonal ring of pendula

TL;DR

This paper demonstrates tunable spin-orbit coupling in a hexagonal ring of pendula through pre-tensioned springs, connecting classical mechanical systems to quantum-like topological phenomena.

Contribution

It introduces a classical mechanical analogue of spin-orbit coupling in a hexagonal pendula system, both theoretically and experimentally, with potential for exploring topological effects.

Findings

Experimental frequencies match theoretical predictions

Eigenmodes exhibit spin-like degrees of freedom

Tunable spin-orbit coupling observed in the system

Abstract

We consider the mechanical motion of a system of six macroscopic pendula which are connected with springs and arranged in a hexagonal geometry. When the springs are pre-tensioned, the coupling between neighbouring pendula along the longitudinal (L) and the transverse (T) directions are different: identifying the motion along the L and T directions as a spin-like degree of freedom, we theoretically and experimentally verify that the pre-tensioned springs result in a tunable spin-orbit coupling. We elucidate the structure of such a spin-orbit coupling in the extended two-dimensional honeycomb lattice, making connections to physics of graphene. The experimental frequencies and the oscillation patterns of the eigenmodes for the hexagonal ring of pendula are extracted from a spectral analysis of the motion of the pendula in response to an external excitation and are found to be in good agreement with our theoretical predictions. We anticipate that extending this classical analogue of quantum mechanical spin-orbit coupling to two-dimensional lattices will lead to exciting new topological phenomena in classical mechanics.