Heat Capacity of a Strongly-Interacting Fermi Gas

We report on the measurement of the heat capacity for an optically-trapped, strongly-interacting Fermi gas of atoms. For a precisely controlled energy input, we fit the spatial density of the cloud to a Thomas-Fermi distribution. We show that the fits define a reduced temperature $\tilde{T} =T/(T_F\sqrt{1+\beta})$, where $\beta$ is the universal parameter introduced by O'Hara et al.,~\cite{OHaraScience}. At $\tilde{T}=0.33$, we observe a transition between two patterns of behavior: For $\tilde{T}=0.33-2.15$, we find that the heat capacity closely corresponds to that of a trapped Fermi gas of noninteracting atoms with the mass scaled by $1/(1+\beta)$. At low temperatures $\tilde{T}=0.04-0.33$, the heat capacity scales as $\tilde{T}^\alpha$, where $\alpha=1.53(0.15)$, corresponding to bosonic (fermion pair) excitations of a condensate.