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

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