  We calculate the spectrum of the scattered light from quantum degenerate
atomic gases obeying Bose-Einstein statistics. The atoms are assumed to occupy
two ground states which are optically coupled through a common excited state by
two low intensity off-resonant light beams. In the presence of a Bose
condensate in both ground states, the atoms may exhibit light induced
oscillations between the two condensates analogous to the Josephson effect. The
spectrum of the scattered light is calculated in the limit of a low oscillation
frequency. In the spectrum we are able to observe qualitative features
depending on the phase difference between the macroscopic wave functions of the
two condensates. Thus, our optical scheme could possibly be used as an
experimental realization of the spontaneous breakdown of the U(1) gauge
symmetry in the Bose-Einstein condensation.
