Spin fragmentation of Bose-Einstein condensates with antiferromagnetic interactions


We study spin fragmentation of an antiferromagnetic spin 1 condensate in the presence of a quadratic Zeeman (QZ) effect breaking spin rotational symmetry. We describe how the QZ effect turns a fragmented spin state, with large fluctuations of the Zeemans populations, into a regular polar condensate, where atoms all condense in the m=0m=0 state along the field direction. We calculate the average value and variance of the Zeeman state m=0m=0 to illustrate clearly the crossover from a fragmented to an unfragmented state. The typical width of this crossover is q∼kBT/Nq \sim k_B T/N, where qq is the QZ energy, TT the spin temperature and NN the atom number. This shows that spin fluctuations are a mesoscopic effect that will not survive in the thermodynamic limit N→∞N\rightarrow \infty, but are observable for sufficiently small atom number.Comment: submitted to NJ

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