  We study symmetry breaking at the Dicke quantum phase transition by coupling
a motional degree of freedom of a Bose-Einstein condensate to the field of an
optical cavity. Using an optical heterodyne detection scheme we observe
symmetry breaking in real-time and distinguish the two superradiant phases. We
explore the process of symmetry breaking in the presence of a small
symmetry-breaking field, and study its dependence on the rate at which the
critical point is crossed. Coherent switching between the two ordered phases is
demonstrated.
