Spontaneous Symmetry Breaking and Defect Formation in a Quenched Ferromagnetic Spinor Bose-Einstein Condensate

We observe spontaneous symmetry breaking in a spinor Bose condensate of $^{87}$Rb that is quenched across a quantum phase transition to a ferromagnetic state. Using high spatial resolution maps of the vector magnetization of the condensate, we directly observe the spontaneous formation of inhomogeneous ferromagnetic regions separated by un-magnetized defects. The growth of these ferromagnetic regions are due to a dynamical instability, which determines their typical size and the time for their formation in accord with our observations.