The Equation of State of a Low-Temperature Fermi Gas with Tunable
  Interactions

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Abstract

Interacting fermions are ubiquitous in nature and understanding their thermodynamics is an important problem. We measure the equation of state of a two-component ultracold Fermi gas for a wide range of interaction strengths at low temperature. A detailed comparison with theories including Monte-Carlo calculations and the Lee-Huang-Yang corrections for low-density bosonic and fermionic superfluids is presented. The low-temperature phase diagram of the spin imbalanced gas reveals Fermi liquid behavior of the partially polarized normal phase for all but the weakest interactions. Our results provide a benchmark for many-body theories and are relevant to other fermionic systems such as the crust of neutron stars.

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Most cited references 25

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Many-Body Problem in Quantum Mechanics and Quantum Statistical Mechanics

T D Lee, C. N. Yang (1957)

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Observation of Fermi Polarons in a Tunable Fermi Liquid of Ultracold Atoms

Cheng-Hsun Wu, André Schirotzek, Ariel Sommer … (2009)

We have observed Fermi polarons, dressed spin down impurities in a spin up Fermi sea of ultracold atoms. The polaron manifests itself as a narrow peak in the impurities' rf spectrum that emerges from a broad incoherent background. We determine the polaron energy and the quasiparticle residue for various interaction strengths around a Feshbach resonance. At a critical interaction, we observe the transition from polaronic to molecular binding. Here, the imbalanced Fermi liquid undergoes a phase transition into a Bose liquid coexisting with a Fermi sea.

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Exploring the Thermodynamics of a Universal Fermi Gas

Christophe Salomon, Sylvain Nascimbene, Nir Navon … (2009)

From sand piles to electrons in metals, one of the greatest challenges in modern physics is to understand the behavior of an ensemble of strongly interacting particles. A class of quantum many-body systems such as neutron matter and cold Fermi gases share the same universal thermodynamic properties when interactions reach the maximum effective value allowed by quantum mechanics, the so-called unitary limit [1,2]. It is then possible to simulate some astrophysical phenomena inside the highly controlled environment of an atomic physics laboratory. Previous work on the thermodynamics of a two-component Fermi gas led to thermodynamic quantities averaged over the trap [3-5], making it difficult to compare with many-body theories developed for uniform gases. Here we develop a general method that provides for the first time the equation of state of a uniform gas, as well as a detailed comparison with existing theories [6,14]. The precision of our equation of state leads to new physical insights on the unitary gas. For the unpolarized gas, we prove that the low-temperature thermodynamics of the strongly interacting normal phase is well described by Fermi liquid theory and we localize the superfluid transition. For a spin-polarized system, our equation of state at zero temperature has a 2% accuracy and it extends the work of [15] on the phase diagram to a new regime of precision. We show in particular that, despite strong correlations, the normal phase behaves as a mixture of two ideal gases: a Fermi gas of bare majority atoms and a non-interacting gas of dressed quasi-particles, the fermionic polarons [10,16-18].