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We have experimentally investigated the quench dynamics of antiferromagneticspinor Bose-Einstein condensates in the vicinity of a zero temperature quantumphase transition at zero quadratic Zeeman shift $q$. The rate of instabilityshows good agreement with predictions based upon solutions to the Bogoliubovde-Gennes equations. A key feature of this work was removal of magnetic fieldinhomogeneities, resulting in a steep change in behavior near the transitionpoint. The quadratic Zeeman shift at the transition point was resolved to 250milliHertz uncertainty, equivalent to an energy resolution of $k_B \times 12$picoKelvin. To our knowledge, this is the first demonstration of sub-Hzprecision measurement of a phase transition in quantum gases. Our results pointto the use of dynamics, rather than equilibrium studies for high precisionmeasurements of phase transitions in quantum gases.

Precise measurements on a quantum phase transition in antiferromagnetic spinor Bose-Einstein condensates