Phase sensitive measurements of order parameters for ultracold atoms through two particles interferometry

Nontrivial symmetry of the pair wave function is crucial to some of the most interesting states of ultracold atoms, including p-wave Feshbach molecules and d-wave paired states of fermions in optical lattices. Identifying these states in experiments requires measurements of the relative phase of different components of the pair wave function. We discuss a new method for such measurements based on two photon interference and noise correlations analysis in the time of flight experiments. Furthermore, in order to unambiguously determine the symmetry of the wave functions, we propose the method analogous to classical white fringe, which can reveal the existence of fundamental phase factors.