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

Nontrivial symmetry of order parameters is crucial in some of the most interesting quantum many-body states of ultracold atoms and condensed matter systems. Examples in cold atoms include p-wave Feshbach molecules and d-wave paired states of fermions that could be realized in optical lattices in the Hubbard regime. Identifying these states in experiments requires measurements of the relative phase of different components of the entangled pair wavefunction. We propose and discuss two schemes for such phase sensitive measurements, based on two-particle interference revealed in atom-atom or atomic density correlations. Our schemes can also be used for relative phase measurements for non-trivial particle-hole order parameters, such as d-density wave order.