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Stokes parameter formalism is applied to show the analogies between themotion of an asymmetric Foucault pendulum and several phenomena known fromoptics and atomic physics. Nonlinearity-induced precession of elliptical orbitsof the pendulum is shown to correspond to twisting transformations used forspin squeezing of atomic systems. Transitions between regimes of predominantnonlinearity and regimes where the Coriolis force or the asymmetry of thependulum are dominant correspond to quantum phase transitions in theLipkin-Meshkov-Glick model. A Foucault pendulum with highly anisotropic dampingcan emulate an optical Zeno effect where a sequence of polarizing filtersinhibits polarization rotation of light in an optically active medium.

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