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

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.