Spontaneous Pattern Formation in an Antiferromagnetic Quantum Gas

In this Letter we report on the spontaneous formation of surprisingly regular periodic magnetic patterns in an antiferromagnetic Bose-Einstein condensate (BEC). The structures evolve within a quasi-one-dimensional BEC of {sup 87}Rb atoms on length scales of a millimeter with typical periodicities of 20...30 {mu}m, given by the spin healing length. We observe two sets of characteristic patterns which can be controlled by an external magnetic field. We identify these patterns as linearly unstable modes within a mean-field approach and calculate their mode structure as well as time and energy scales, which we find to be in good agreement with observations. These investigations open new prospects for controlled studies of symmetry breaking and complex quantum magnetism in bulk BEC.