How to fix a broken symmetry: Quantum dynamics of symmetry restoration in a ferromagnetic Bose-Einstein condensate

TL;DR

This paper investigates the quantum dynamics of symmetry restoration in a spin-1 Bose-Einstein condensate during a phase transition, analyzing non-equilibrium effects, magnetization oscillations, and scaling laws near the critical point.

Contribution

It applies the quantum Kibble-Zurek scheme to a spinor BEC, providing new insights into symmetry restoration dynamics and magnetization behavior during quantum phase transitions.

Findings

Magnetization exhibits nonlinear oscillations at the critical point.

Oscillation amplitude and period are inversely proportional.

Scaling laws relate magnetization to quench rate.

Abstract

We discuss the dynamics of a quantum phase transition in a spin-1 Bose-Einstein condensate when it is driven from the magnetized broken-symmetry phase to the unmagnetized ``symmetric'' polar phase. We determine where the condensate goes out of equilibrium as it approaches the critical point, and compute the condensate magnetization at the critical point. This is done within a quantum Kibble-Zurek scheme traditionally employed in the context of symmetry-breaking quantum phase transitions. Then we study the influence of the nonequilibrium dynamics near a critical point on the condensate magnetization. In particular, when the quench stops at the critical point, nonlinear oscillations of magnetization occur. They are characterized by a period and an amplitude that are inversely proportional. If we keep driving the condensate far away from the critical point through the unmagnetized ``symmetric'' polar phase, the amplitude of magnetization oscillations slowly decreases reaching a non-zero asymptotic value. That process is described by the equation that can be mapped onto the classical mechanical problem of a particle moving under the influence of harmonic and ``anti-friction'' forces whose interplay leads to surprisingly simple fixed-amplitude oscillations. We obtain several scaling results relating the condensate magnetization to the quench rate, and verify numerically all analytical predictions.