The understanding of physical properties of fermions in the unitary regime, where the s-wave scattering length in the collisional channel of particles is longer than both the interparticle distance and the size of the interaction potential, is a crucial issue for electron systems of high-temperature superconductivity, dilute nucleons in nuclei, and neutron stars. We experimentally determine various thermodynamic quantities of interacting two-component fermions at the zero-temperature limit from the BCS region to the unitarity limit. The obtained results are very accurate in the sense that the systematic error is within 4% in the unitary regime. Using this advantage, we can compare our data with various many-body theories. We find that an extended T-matrix approximation, which is a strong-coupling theory involving fluctuations in the Cooper channel, well reproduces our experimental results. We also find that the superfluid order parameter Δ calculated by solving the ordinary BCS gap equation with the chemical potential of interacting fermions is close to the binding energy of the paired fermions directly observed in a spectroscopic experiment and that obtained using a quantum Monte Carlo method.
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