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We study strongly interacting two component Fermi gas near a Feshbachresonance. By using a ground state energy functional constructed based onasymptotic limits and Monte Carlo calculations, we calculate the contact,structure factor, and collective oscillation frequencies in the BCS-BECcrossover region. The calculated contact and structure factor show excellentagreements with recent experiments. We compare these results with a standardmean-field theory and find that the contact is proportional to the square ofsuperfluid order parameter. Further, we present the chemical potential and thepolytropic index in terms of homogenous energy and the contact.

Tan's universal contact and collective oscillations of strongly interacting Fermi gases