Probing many-body states of ultracold atoms via noise correlations

We propose to utilize density-density correlations in the image of an expanding gas cloud to probe complex many-body states of trapped ultracold atoms. In particular, we show how this technique can be used to detect superfluidity of fermionic gases and to study spin correlations of multicomponent atoms in optical lattices. The feasibility of the method is investigated by analysis of the relevant signal to noise ratio including experimental imperfections.