Noise correlations in one-dimensional systems of ultracold fermions

Time of flight images reflect the momentum distribution of the atoms in the trap, but the spatial noise in the image holds information on more subtle correlations. Using bosonization, we study such correlations in generic 1D systems of ultracold fermions. We show how pairing as well as spin and charge density wave correlations may be identified and extracted from time of flight images. These incipient orders manifest themselves as power-law singularities in the noise correlations, that depend on the Luttinger parameters, which suggests a general experimental technique to obtain them.