We investigate, both experimentally and theoretically, the quench dynamics of antiferromagnetic spinor Bose-Einstein condensates in the vicinity of a zero temperature quantum phase transition at zero quadratic Zeeman shift q. Both the rate of instabi
lity and the associated finite wavevector of the unstable modes - show good agreement with predictions based upon numerical solutions to the Bogoliubov de-Gennes equations. A key feature of this work is inclusion of magnetic field inhomogeneities that smooth the phase transition. Once these were removed, we observed a dramatic sharpening of the transition point, which could then be resolved within a quadratic Zeeman shift of only 1-2 Hz. Our results point to the use of dynamics, rather than equilibrium quantities for high precision measurements of phase transitions in quantum gases.
The possibility to coherently control a quantum rotor is investigated theoretically. The rotor is realized by an antiferromagnetic spin-1 Bose-Einstein condensate, trapped in the optical field of a Fabry-Perot resonator. By tuning the pumping field o
f the resonator, coherent control over the rotor is achieved. The technique is illustrated by the numerical simulation of a protocol that transforms the rotors ground state into a squeezed state. The detection of the squeezed state via measurement of intensity-correlations of the cavity field is proposed.
