  For bosons, the transition rate into an already occupied quantum state is
enhanced by its occupation number: the effect of bosonic stimulation. Bosonic
enhancement of light scattering has been predicted more than 30 years ago but
has not been observed before. Here we theoretically investigate and
experimentally demonstrate this effect. We show that the bosonic enhancement
factor for a harmonically trapped gas is bounded by a universal constant
$\zeta(2)/\zeta(3)$ above the phase transition to a Bose-Einstein condensate
(BEC), and depends linearly on the BEC fraction just below the phase
transition. Bosonically enhanced light scattering is observed and characterized
above and below the phase transition, and the effect of interactions is
discussed. For a multi-level system, bosonic enhancement is reduced because
bosonic stimulation occurs only for Rayleigh scattering, but not for Raman
scattering.
