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arXiv:1110.3309 · Science

Revealing the Superfluid Lambda Transition in the Universal Thermodynamics of a Unitary Fermi Gas

Mark Ku, Ariel Sommer, Lawrence W. Cheuk, Martin W. Zwierlein

Published Jan 13, 2012• 711 citations
arXivHTMLPDF

Abstract

Fermi gases, collections of fermions such as neutrons and electrons, are found throughout nature, from solids to neutron stars. Interacting Fermi gases can form a superfluid or, for charged fermions, a superconductor. We have observed the superfluid phase transition in a strongly interacting Fermi gas by high-precision measurements of the local compressibility, density, and pressure. Our data completely determine the universal thermodynamics of these gases without any fit or external thermometer. The onset of superfluidity is observed in the compressibility, the chemical potential, the entropy, and the heat capacity, which displays a characteristic lambda-like feature at the critical temperature T(c)/T(F) = 0.167(13). The ground-state energy is 3/5ξN E(F) with ξ = 0.376(4). Our measurements provide a benchmark for many-body theories of strongly interacting fermions.

DOI
10.1126/science.1214987

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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.
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.
We will present recent experimental work on the thermodynamics of strongly interacting Fermi gases. We have developed a general method to probe with high precision the Equation of State (EoS) of locally homogeneous ultracold gases. This allows stringent tests of recent many-body theories. First, we focus on the finite-temperature EoS of the unpolarized unitary gas. Precise thermometry is provided by adding to the Fermi gas of 6Li a trace of bosonic 7Li. We show that the low-temperature properties of the strongly interacting normal phase are well described by Fermi liquid theory and we localize the superfluid transition. Second, we address the zero-temperature EoS of the spin-polarized system in the BEC-BCS crossover. Surprisingly, despite strong interactions, the polarized phase behaves as a mixture of two ideal gases: a Fermi gas of majority atoms and a non-interacting gas of dressed quasi-particles, the Fermi polarons. We also obtain the equation of state of the superfluid state as a function of interaction strength, that we compare to Monte Carlo simulations and to the Lee-Huang-Yang corrections for low-density bosonic and fermionic superfluids.
transition, critical parameters Abstract Strongly interacting Fermi gases provide a clean and controllable laboratory system for modeling strong interparticle interactions between fermions in nature, from high temperature superconductors to neutron matter and quark-gluon plasmas. Model-independent thermodynamic measurements, which do not require theoretical models for calibrations, are very important for exploring this important system experimentally, as they enable direct tests of predictions based on the best current non-perturbative many-body theories. At Duke University, we use all-optical methods to produce a strongly interacting Fermi gas of spin-1/2-up and spin-1/2-down 6 Li atoms that is magnetically tuned near a collisional (Feshbach) resonance. We conduct a series of measurements on the thermodynamic properties of this unique quantum gas, including the energy E, entropy S, and sound velocity c. Our model-independent measurements of E and S enable a precision study of the finite temperature thermodynamics. The E(S) data are directly compared to several recent predictions. The temperature in both the superfluid and normal fluid