Probing Phase Transitions in Cold Atoms

In this talk I will describe various interferometric probes, which can be used to study correlation functions of low-dimensional cold atom systems. These probes allow one to analyze both properties of phases with long or quasi-long range order and phase transitions. I will suggest the way of detecting fermionic superfluidity and the symmetry of the pairing gap. I will also discuss connections between interferometry in 1D bosonic systems with partition functions of some condensed matter models and with extreme value statistics. Finally I will describe the shot noise and argue how one can suppress it both for bosons and fermions using optical lattices.