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arXiv:1001.2085 · New Journal of Physics

Universal thermodynamics of a strongly interacting Fermi gas: theory versus experiment

Hui Hu, Xia-Ji Liu, P. D. Drummond

Published Jun 30, 2010• 72 citations

Abstract

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.

DOI: 10.1088/1367-2630/12/6/063038

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Latin America Optics and Photonics Conference•Jan 1, 2010•5 citations

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 recently discovered universal thermodynamic behavior of dilute, strongly interacting Fermi gases also implies a universal structure in the many-body pair-correlation function at short distances, as quantified by the contact . Here, we theoretically calculate the temperature dependence of this universal contact for a Fermi gas in free space and in a harmonic trap. At high temperatures above the Fermi degeneracy temperature, T ≳ T F , we obtain a reliable non-perturbative quantum virial expansion up to third order. At low temperatures, we compare different approximate strong-coupling theories. These make different predictions, which need to be tested either by future experiments or by advanced quantum Monte Carlo simulations. We conjecture that in the universal unitarity limit, the contact or correlation decreases monotonically with increasing temperature, unless the temperature is significantly lower than the critical temperature, T ≪ T c ∼0.2 T F . We also discuss briefly how to measure the universal contact in either homogeneous or harmonically trapped Fermi gases.

We compare the theoretical predictions for universal thermodynamics of a homogeneous, strongly correlated Fermi gas with the latest experimental measurements reported by the ENS group [S. Nascimb\`ene et al., Nature (London) 463, 1057 (2010)] and the Tokyo group [M. Horikoshi et al., Science 327, 442 (2010)]. The theoretical results are obtained using two diagrammatic theories, together with a virial expansion theory combined with a P\'ade approximation. We find good agreement between theory and experiment. In particular, the virial expansion, using a P\'ade approximation up to third order, describes the experimental results extremely well down to the superfluid transition temperature,

{T}_{c}~0.16{T}_{F}

, where

{T}_{F}

is the Fermi temperature. The comparison in this work complements our previous comparative study on the universal thermodynamics of a strongly correlated but trapped Fermi gas. The comparison also raises interesting issues about the unitary entropy and the applicability of the P\'ade approximation.

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

Understanding the formation of Cooper pairs and the resulting thermodynamic properties of low-dimensional Fermi gases is an important area of research, which may help build our understanding of other low-dimensional systems, such as high-temperature superconductors. In lower dimensions, quantum fluctuations are expected to play an increasingly important role, and the reliability of strong-coupling theories becomes questionable. Here, we present a comparison of recent thermodynamic measurements and theoretical predictions from different many-body

T

-matrix theories for a two-dimensional strongly interacting Fermi gas in the normal state. We find that the fully self-consistent

T

-matrix theory provides the best description of the experimental data over a wide range of temperatures and interatomic interactions.

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.