Study of geometric phase using classical coupled oscillators

TL;DR

This paper demonstrates how classical coupled oscillators can exhibit a geometric phase during cyclic evolution, using an analogy with quantum systems to visualize phase changes on a spherical surface.

Contribution

It introduces a classical analog for the quantum geometric phase using coupled oscillators and proposes an accessible experiment for students to observe this phenomenon.

Findings

Classical coupled oscillators can exhibit a geometric phase.

The phase change can be visualized on a spherical surface.

An experimental setup for students to observe the geometric phase.

Abstract

We illustrate the geometric phase associated with the cyclic dynamics of a classical system of coupled oscillators. We use an analogy between a classical coupled oscillator and a two-state quantum mechanical system to represent the evolution of the oscillator on an equivalent Hilbert space, which may be represented as a trajectory on the surface of a sphere. The cyclic evolution of the system leads to a change in phase, which consists of a dynamic phase along with an additional phase shift dependent on the geometry of the evolution. A simple experiment suitable for advanced undergraduate students is designed to study the geometric phase incurred during cyclic evolution of a coupled oscillator.