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Journal of Physics Conference Series

Thermodynamics of the unitary Fermi gas

Frédéric Chevy, Sylvain Nascimbène, Nir Navon, Kaijun Jiang, C Lobo, Ch Salomon

Published Jan 10, 2011• 3 citations
Publisher

Abstract

The understanding of quantum many-body systems is one of the most daunting challenges of modern physics. Thanks to recent progress in cooling and trapping techniques, it is now possible to investigate their properties in the well controlled environment of ultra-cold gas systems. In this article, we present experimental results on the thermodynamics of strongly correlated Fermi gases and we provide a reinterpretation of the equation of state of a strongly polarized Fermi gas in terms of Fermi liquid parameters

DOI
10.1088/1742-6596/264/1/012012

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The understanding of quantum many-body systems is one of the most daunting challenges of modern physics. Thanks to recent progress in cooling and trapping techniques, it is now possible to investigate their properties in the well controlled environment of ultra-cold gas systems. In this article, we present experimental results on the thermodynamics of strongly correlated Fermi gases and we provide a reinterpretation of the equation of state of a strongly polarized Fermi gas in terms of Fermi liquid parameters
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.
We briefly review current research progress in the field of strongly correlated atomic Fermi gases. A deep understanding of strongly correlated quantum gases is plagued by the lack of either exact solutions or a controllable small interaction parameter. In this work, we present a systematic virial expansion method to study the high-temperature thermodynamics of a strongly correlated Fermi gas,where the controllable parameter is given by the fugacity,exp (μkBT),with μ being the chemical potential. A practical way is proposed to obtain the expansion coefficients for both homogeneous and harmonically trapped Fermi gases. We calculate, for the first time accurately, the third-order virial coefficient. The resulting equation of states at high temperatures is compared with a recent thermodynamic measurement and with Monte Carlo simulations.
Strongly interacting, dilute Fermi gases exhibit a scale-invariant, universal thermodynamic behavior. This is notoriously difficult to understand theoretically because of the absence of a small interaction parameter. Here, we present a systematic comparison of theoretical predictions from different quantum many-body theories with recent experimental data of Nascimbne et al (2010 Nature 463 1057). Our comparisons have no adjustable parameters, either theoretically or experimentally. All the model approximations seem to fluctuate rather than converge on the experimental data. It turns out that a simple Gaussian pair fluctuation theory gives the best quantitative agreement, except at the critical superfluid transition region. In the normal state, we also calculate the equation of state by using a quantum cluster expansion theory and explore in detail its applicability to low temperatures. Using the accurate experimental result for the thermodynamic function S ( T ), we determine the temperature T of a trapped Fermi gas at unitarity as a function of a non-interacting temperature T i , which can be obtained by an adiabatic sweep to the free gas limit. By analyzing the recent experimental data, we find a characteristic temperature ( T / T F ) 0 =0.19±0.02 or ( T i / T F ) 0 =0.16±0.02 in a harmonic trap, below which there are deviations from normal Fermi-liquid-like behavior that may be attributed to pairing effects. Here, T F is the Fermi temperature for a trapped ideal, non-interacting Fermi gas. Our thorough comparison may shed light on the further theoretical development of strongly interacting fermions.
The quantum many-body problem is at the heart of some of the most formidable open problems in modern physics, such as high-Tc_cc​ superconductivity or the behaviour of neutron stars. Ultracold atomic systems can now be used to simulate model Hamiltonians of condensed matter or nuclear physics, in very well-controlled environnement. In this thesis, we have developed a general method to probe the thermodynamics of homogeneous quantum systems using trapped atomic gases. These measurements are directly compared to the predictions of theories of the quantum many-body problem. We have applied this technique to the spin-1/21/21/2 Fermi gas and the Bose with short-range interactions. Using fermionic 6^66Li, we explored a part of the wide parameter space by changing the interaction strength, the spin-population imbalance or the temperature of the gas. This system exhibits remarkably rich physics, such as normal/superfluid phase transitions (that can be of thermal or quantum character) or a Fermi liquid-type behaviour of the normal phase. We have also used this method to probe a Bose gas of 7^77Li atoms close to a Feshbach resonance. We have measured the Equation of State of the Bose gas as a function of interactions at very low temperature. For the first time, we measured quantitatively the Lee-Huang-Yang beyond mean-field correction to the ground-state energy of the system, first predicted in 1957. We compared the experimental results to Quantum Monte-Carlo calculations. We have extended this study using out-of-equilibrium measurements of the Bose gas in the strongly interacting regime, which gives a first hint on the properties of the hypothetical unitary Bose gas.
Ultra-cold atomic Fermi gases at nano-Kelvin temperatures provide a new paradigm for the foundations of quantum many-body theory. Here, we summarize our recent theoretical efforts to understand the intriguing properties of these strongly correlated Fermi gases. A number of powerful theoretical techniques have been developed, including (i) a quantitative diagrammatic theory taken to infinite order; (ii) a virial expansion at high temperature; (iii) exact solutions for one-dimensional many-body systems; and (iv) new quantum simulations using the Gaussian Fermi representation. We have employed these techniques to predict universal thermodynamics in the strongly interacting limit and exotic quantum superfluid phases with imbalanced spin populations. More insights into strongly interacting Fermi gases are anticipated, by extending the Gaussian Fermi simulations to new regimes.
We show how Fermi liquid theory can be applied to ultra-cold Fermi gases and propose a way to extract the position dependent effective mass and Landau parameters F0s(r)F_{0}^{s}(r)F0s​(r) and F0a(r)F_{0}^{a}(r)F0a​(r) from the experimental trap profiles, within the local density approximation. We outline the signatures for a Fermi liquid thereby addressing the recent claim that the normal state of a unitary gas is a Fermi liquid phase; this controversial claim counters other evidence for a non-Fermi liquid phase. Understanding these Fermi liquid signatures also bears on recent controversies over the nature of alternative ground states in a (possibly ferromagnetic) Fermi Hubbard gas.