Asymmetric Foucault pendulum dynamics with analogies to the Lipkin-Meshkov-Glick quantum phase transitions and other quantum phenomena

TL;DR

This paper explores the analogies between asymmetric Foucault pendulum dynamics and quantum phenomena, revealing how classical pendulum behavior can emulate complex quantum phase transitions and effects.

Contribution

It introduces a novel analogy framework linking pendulum motion to quantum phase transitions and optical phenomena, expanding understanding of classical-quantum correspondences.

Findings

Pendulum precession corresponds to spin squeezing transformations.

Transitions in pendulum regimes mimic quantum phase transitions.

Highly anisotropic damping emulates the optical Zeno effect.

Abstract

Stokes parameter formalism is applied to show the analogies between the motion of an asymmetric Foucault pendulum and several phenomena known from optics and atomic physics. Nonlinearity-induced precession of elliptical orbits of the pendulum is shown to correspond to twisting transformations used for spin squeezing of atomic systems. Transitions between regimes of predominant nonlinearity and regimes where the Coriolis force or the asymmetry of the pendulum are dominant correspond to quantum phase transitions in the Lipkin-Meshkov-Glick model. A Foucault pendulum with highly anisotropic damping can emulate an optical Zeno effect where a sequence of polarizing filters inhibits polarization rotation of light in an optically active medium.