Euler top with a rotor: classical analogies of spin squeezing and quantum phase transitions in a generalized Lipkin-Meshkov-Glick model

TL;DR

This paper establishes a classical-quantum analogy using the Euler top with a rotor to model and explore quantum phenomena like spin squeezing, quantum phase transitions, and Floquet time crystals within a generalized Lipkin-Meshkov-Glick framework.

Contribution

It introduces a classical model that parallels complex quantum effects, expanding understanding of quantum phase transitions and time crystals through classical analogies.

Findings

Classical effects correspond to quantum phenomena such as spin squeezing and phase transitions.

The analogy broadens the exploration of quantum critical phenomena.

A classical analogy of the LMG Floquet time crystal is presented.

Abstract

We show that the classical model of Euler top (freely rotating, generally asymmetric rigid body), possibly supplemented with a rotor, corresponds to a generalized Lipkin-Meshkov-Glick (LMG) model describing phenomena of various branches of quantum physics. Classical effects such as free precession of a symmetric top, Feynman's wobbling plate, tennis-racket instability and the Dzhanibekov effect, attitude control of satellites by momentum wheels, or twisting somersault dynamics, have their counterparts in quantum effects that include spin squeezing by one-axis twisting and two-axis countertwisting, transitions between the Josephson and Rabi regimes of a Bose-Einstein condensate in a double-well potential, and other quantum critical phenomena. The parallels enable us to expand the range of explored quantum phase transitions in the generalized LMG model, as well as to present a classical analogy of the recently proposed LMG Floquet time crystal.