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 the two components of 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.
Highlights
The topological effects that underlie intriguing quantum mechanical phenomena, such as the quantum Hall effect, are not the prerogative of quantum mechanical systems, but have recently been observed in classical systems governed by Newton’s equations [1]
In this paper we have given experimental evidence for a tunable spin–orbit coupling in classical mechanics using a system of six coupled pendula arranged in a hexagonal geometry and connected by pre-tensioned springs
The experimental results for the oscillation frequencies and the oscillation patterns are compared with theoretical models: while the qualitative agreement with a simple pendulum approximation is already quite good, it becomes quantitatively excellent once we take into account the finite radius of the masses and their rotation around the hook connecting them to the string
Summary
We consider the mechanical motion of a system of six macroscopic pendula which are connected with author(s) and the title of springs and arranged in a hexagonal geometry. When the springs are pre-tensioned, the coupling the work, journal citation and DOI. Between neighbouring pendula along the longitudinal (L) and the transverse (T) directions are different: identifying the motion along the L and T directions as the two components of 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. 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
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