Measurement of Universal Thermodynamic Functions for a Unitary Fermi Gas

Abstract

Thermodynamic properties of matter generally depend on the details of interactions between its constituent parts. However, in a unitary Fermi gas where the scattering length diverges, thermodynamics is determined through universal functions that depend only on the particle density and temperature. By using only the general form of the equation of state and the equation of force balance, we measured the local internal energy of the trapped gas as a function of these parameters. Other universal functions, such as those corresponding to the Helmholtz free energy, chemical potential, and entropy, were calculated through general thermodynamic relations. The critical parameters were also determined at the superfluid transition temperature. These results apply to all strongly interacting fermionic systems, including neutron stars and nuclear matter.

Thermodynamics of Ultracold Fermi Gases

“…This lower bound nearly coincides with the temperature at which a part of the gas becomes super uid [43,46,39,47]. Therefore this thermometer is not suited for investigating low-temperature e ects in the super uid phase.…”

“…The thermodynamics of a homogeneous unitary Fermi gas was experimentally studied, simultaneously to our work, by the Tokyo group [47]. Using the equation of state of a trapped unitary gas measured in the Duke group [63] as a reference for thermometry, they obtain a canonical equation of state for the homogeneous gas, from the analysis of density pro les after a hydrodynamic expansion (see Fig.4.8a).…”

“…In order to test the robustness of this procedure, we calculated the chemical potential of an ideal gas using the experimental equation of state of an ideal gas also measured in [47] (see Fig.4.8a). As shown in Fig.4.8b, the chemical potential deduced from the experimental data agrees with the theoretical chemical potential of an ideal gas.…”

“…The connection with Bose-Einstein condensation was characterized by a direct measurement of the condensate fraction [35,36,47], and the importance of many-body e ects was established through the measurement of the single-particle excitation energy gap [50,51] and closed-channel fraction [38].…”

Spin Susceptibility and Effects of Inhomogeneous Strong Pairing Fluctuations in a Trapped Ultracold Fermi Gas

“…A uniform Fermi gas at the unitarity is known to exhibit the so-called universal thermodynamics 31,32,33 , where the Fermi energy ε F (or equivalently the Fermi temperature T F ) is the unique energy scale, because of the vanishing inverse scattering length a −1 s = 0. In the present trapped case, the scaled local spin susceptibility in LDA is expected to behave as,…”