Noise correlations of the ultracold Fermi gas in an optical lattice

In this paper we study the density noise correlations of the two component Fermi gas in optical lattices. Three different types of phases, the BCS state (Bardeen, Cooper, and Schieffer), the FFLO state (Fulde, Ferrel, Larkin, and Ovchinnikov), and the BP (breach pair) state are considered. We show how these states differ in their noise correlations. The noise correlations are calculated not only at zero temperature, but also at nonzero temperatures paying particular attention to how much the finite temperature effects might complicate the detection of different phases. Since one-dimensional systems have been shown to be very promising candidates to observe FFLO states, we apply our results also to the computation of correlation signals in a one-dimensional lattice. We find that the density noise correlations reveal important information about the structure of the underlying order parameter as well as about the quasiparticle dispersions.