Revealing the superfluid phase transition in strongly interacting Fermi gases in a precision measurement of the equation of state*

We perform a high-precision measurement of the equation of state (EOS) of a Fermi gas at unitarity by in-situ imaging of ultracold $^6$Li at a Feshbach resonance. The reconstructed local density distribution directly probes the EOS under the local density approximation. We extract the chemical potential and the temperature from low density regions via the virial expansion, and validate our method using the non-interacting Fermi gas. The experimental results are compared to recent Monte-Carlo calculations. We observe the superfluid transition in the chemical potential, entropy, compressibility and heat capacity, which display characteristic lambda-like features. We provide a new value of the Bertsch parameter $\xi_S$ and directly obtain the critical temperature from the EOS, validated via a condensate fraction measurement.