Noise Correlations in one-dimensional systems of ultra-cold 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 noise correlations in generic one dimensional systems of ultra cold fermions. Specifically, we show how pairing as well as spin and charge density wave correlations may be identified and extracted from the 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.Comment: 5 pages, 3 figures. Added discussion on the visibility of noise correlation features for realistic condition

Commensurate mixtures of ultra-cold atoms in one dimension

We study binary mixtures of ultra-cold atoms, confined to one dimension in an optical lattice, with commensurate densities. Within a Luttinger liquid description, which treats various mixtures on equal footing, we derive a system of renormalization group equations at second order, from which we determine the rich phase diagrams of these mixtures. These phases include charge/spin density wave order, singlet and triplet pairing, polaron pairing, and a supersolid phase. Various methods to detect our results experimentally are discussed.Comment: 7 pages, 4 figures, v4: extended versio