  Optical excitations in a Bose gas are demonstrated to be very sensitive to
many-body effects. At low temperature the momentum relaxation is provided by
momentum exchange collisions, rather than by elastic collisions. A collective
excitation mode forms, which in a Boltzmann gas is manifest in a collision
shift and dramatic narrowing of spectral lines.
  In the BEC state, each spectral line splits into two components. The doubling
of the optical excitations results from the physics analogous to that of the
second sound. We present a theory of the line doubling, and calculate the
oscillator strengths and linewidth.
