Precise measurement of phase transitions in spinor Bose-Einstein condensates

We investigate out-of-equilibrium phenomena in sodium spinor Bose-Einstein condensates by studying the evolution of system following a dynamical instability. Sodium condensates are initially prepared in $|F=1,m_F=0 \rangle $ state and are rapidly quenched across a quantum phase transition. It leads to pair formation of $ |F=1,m_F= +1 \rangle $ and $|F=1,m_F=-1 \rangle $ atoms and results in their rapid amplification through spin-mixing instability. We reveal strong tunability of this amplification using magnetic field gradients. We observe a suppression of up to a factor of 10 in instability rates in the neighborhood of the phase transition. These observations show good agreement with predictions based upon numerical solutions to the Bogoliubov de-Gennes equations. We also observe a dramatic sharpening of the quantum phase transition point as magnetic field inhomogenieties are reduced, resulting in a resolution of the phase transition at the 1 Hz level.