Resonant Light Scattering to Measure BEC-Pairing

We present a single-scattering formalism for incoherent resonant light scattering by dilute quantum gas systems such as the atomic-trap Bose-Einstein condensates. We show that resonant scattering gives access to more information than the dynamical structure factor, familiar from non-resonant scattering. In particular, we show that the detuning dependence of the incoherent scattering cross-section allows the direct determination of the BEC pairing density $< \psi \psi >$, which is a broken symmetry and provides evidence that the condensate is not in a good number state.