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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Universal thermodynamics of strongly interacting Fermi gases

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

Published Jun 1, 2007• 3 citations
Publisher

Abstract

The report analyzes all the available experimental data from three laboratories on the entropy-energy relation of two different strongly interacting trapped Fermi gases, and compare this directly with a single universal theoretical prediction. A diagrammatic approach based on functional path-integrals is used together with the local density approximation to treat the inhomogeneous trap. Below the superfiuid transition, the calculations include pairing fluctuations, which are important in the strongly interacting regime, due to the onset of molecule formation.

DOI
10.1109/cleoe-iqec.2007.4386736

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The report analyzes all the available experimental data from three laboratories on the entropy-energy relation of two different strongly interacting trapped Fermi gases, and compare this directly with a single universal theoretical prediction. A diagrammatic approach based on functional path-integrals is used together with the local density approximation to treat the inhomogeneous trap. Below the superfiuid transition, the calculations include pairing fluctuations, which are important in the strongly interacting regime, due to the onset of molecule formation.
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.
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, Tc 0.16TF{T}_{c}~0.16{T}_{F}Tc​ 0.16TF​, where TF{T}_{F}TF​ 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.
The dynamics of strongly interacting trapped dilute two-component Fermi gases (dilute in the sense that the range of interatomic potential is small compared with interparticle spacing) is investigated in a single-equation approach to the time-dependent density-functional theory. For the ground-state energy per particle of the system in the homogeneous phase, we have constructed an Pad\'e parametrization based on Monte Carlo data and asymptotic behavior. Our numerical results for collective frequencies in the BCS-BEC crossover regime are in good agreement with recent experimental data obtained by the Duke University group. In addition, we show that the calculated corrections to the hydrodynamic approximation may be important, even for systems with a rather large number of atoms.
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.
Strongly interacting gases of ultracold fermions have become an amazingly rich test-bed for many-body theories of fermionic matter. Here we present our recent experiments on these systems. Firstly, we discuss high-precision measurements on the thermodynamics of a strongly interacting Fermi gas across the superfluid transition. The onset of superfluidity is directly observed in the compressibility, the chemical potential, the entropy, and the heat capacity. Our measurements provide benchmarks for current many-body theories on strongly interacting fermions. Secondly, we have studied the evolution of fermion pairing from three to two dimensions in these gases, relating to the physics of layered superconductors. In the presence of p-wave interactions, Fermi gases are predicted to display toplogical superfluidity carrying Majorana edge states. Two possible avenues in this direction are discussed, our creation and direct observation of spin-orbit coupling in Fermi gases and the creation of fermionic molecules of 23Na 40K that will feature strong dipolar interactions in their absolute ground state.