Interaction Energy in a Paired Two-Component Degenerate Fermi Gas in the BEC-BCS Crossover

We have measured the interaction energy of the ground-state of a paired Fermi gas in the BEC-BCS crossover. The crossover describes the smooth transition from a BEC of tightly bound dimers to that of a paired BCS superfluid. A Feshbach resonance is used to tune the atomic scattering length \textit{a}. The interaction energy is extracted from \textit{in-situ} images of a trapped two component gas of $^{6}$Li atoms near $T=0$. Near the peak of the Feshbach resonance the interaction energy is expected to be parameterized by a single universal parameter $\beta$ describing a strongly interacting, paired superfluid. We find that $\beta = -0.54$ $\pm$ $0.05$ in good agreement with recent Monte Carlo calculations giving $\beta = -0.58$. On the BEC side of resonance, we find that the molecular scattering length is $0.6 a$, in agreement with recent theory, but only for fields not too close or too far from resonance.