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Bulletin of the American Physical Society

Equation of State of a Strongly Interacting Atomic Fermi Gas

Mark Ku, André Schirotzek, Ariel Sommer, Martin W. Zwierlein, Kris Van Houcke, Félix Werner, Evgeny Kozik, Nikolay V. Prokof'ev, Boris V. Svistunov

Published Mar 18, 2010• 2 citations
OpenAlex

Abstract

distribution in an external potential directly probes the equation of state under the local density approximation. The equation of state is obtained in two ways: from the local density of the gas, reconstructed using the inverse Abel transformation; and from the local pressure, directly deduced from the 2D column density via an exact relation including the Gaussian potential. Regions of low density allow us to extract the chemical potential and the temperature using the virial expansion of the equation of state. We validate our method using the non-interacting Fermi gas. The experimental results are compared to recent Monte-Carlo calculations. 1 AFOSR-MURI, DARPA-OLE, Alfred P. Sloan Foundation, NSF

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<ノート>多体問題とグリーン関数との関係の研究--グリーン関数と多体問題(11)量子統計力学(3)

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ln this paper, next subject is discussed, §32. The equation of state of an ideal gas. Here we consider the equation of state of a spinless ideal Fermi gas. ln high temperatures and low density, we obtain the form of a virial expansion of the equation of state. The corrections to the classical ideal gas law are due to quantum effects. The second virial coefficient is deduced. In low temperature and high densities, we obtain the expansion for the chemical potential in the expansion parameter /<ε_F>. Next we obtain the asynptotic expansion of the internal energyU in the expansion parameter /<ε_F>. We also obtain the specific heat at constant volume C_V.~

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distribution in an external potential directly probes the equation of state under the local density approximation. The equation of state is obtained in two ways: from the local density of the gas, reconstructed using the inverse Abel transformation; and from the local pressure, directly deduced from the 2D column density via an exact relation including the Gaussian potential. Regions of low density allow us to extract the chemical potential and the temperature using the virial expansion of the equation of state. We validate our method using the non-interacting Fermi gas. The experimental results are compared to recent Monte-Carlo calculations. 1 AFOSR-MURI, DARPA-OLE, Alfred P. Sloan Foundation, NSF
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.
Complex Hamiltonians from condensed matter, such as the Fermi-Hubbard model, can be experimentally studied using ultracold gases. This thesis describes a new method for determining the equation of state of an ultracold gas, making the comparison with many-body theories straightforward. It is based on the measurement of the local pressure inside a trapped gas from the analysis of its in situ image. We first apply this method to the study of a Fermi gas with resonant interactions, a weakly-interacting 7Li gas acting as a thermometer. Surprisingly, none of the existing many-body theories of the unitary gas accounts for the equation of state deduced from our study over its full range. The virial expansion extracted from the high-temperature data agrees with the resolution of the three-body problem. At low temperature, we observe, contrary to some previous studies, that the normal phase behaves as a Fermi liquid. Finally we obtain the critical temperature for superfluidity from a clear signature on the equation of state. We also measure the pressure of the ground state as a function of spin imbalance and interaction strength -- measure directly relevant to describe the crust of neutron stars. Our data validate Monte-Carlo simulations and quantify the Lee-Huang-Yang corrections to mean-field interactions in low-density fermionic or bosonic superfluids. We show that, in most cases, the partially polarized normal phase can be described as a Fermi liquid of polarons. The polaron effective mass extracted from the equation of state is in agreement with a study of collective modes.
ln this paper, next subject is discussed, §32. The equation of state of an ideal gas. Here we consider the equation of state of a spinless ideal Fermi gas. ln high temperatures and low density, we obtain the form of a virial expansion of the equation of state. The corrections to the classical ideal gas law are due to quantum effects. The second virial coefficient is deduced. In low temperature and high densities, we obtain the expansion for the chemical potential in the expansion parameter /<ε_F>. Next we obtain the asynptotic expansion of the internal energyU in the expansion parameter /<ε_F>. We also obtain the specific heat at constant volume C_V.~
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.
By using exact path-integral Monte Carlo methods we calculate the equation of state of an interacting Bose gas as a function of temperature both below and above the superfluid transition. The universal character of the equation of state for dilute systems and low temperatures is investigated by modeling the interatomic interactions using different repulsive potentials corresponding to the same sss-wave scattering length. The results obtained for the energy and the pressure are compared to the virial expansion for temperatures larger than the critical temperature. At very low temperatures we find agreement with the ground-state energy calculated using the diffusion Monte Carlo method.
We determine the thermodynamic properties and the spectral function for a homogeneous two-dimensional Fermi gas in the normal state using the Luttinger-Ward, or self-consistent T-matrix, approach. The density equation of state deviates strongly from that of the ideal Fermi gas even for moderate interactions, and our calculations suggest that temperature has a pronounced effect on the pressure in the crossover from weak to strong coupling, consistent with recent experiments. We also compute the superfluid transition temperature for a finite system in the crossover region. There is a pronounced pseudogap regime above the transition temperature: the spectral function shows a Bogoliubov-like dispersion with backbending, and the density of states is significantly suppressed near the chemical potential. The contact density at low temperatures increases with interaction and compares well with both experiment and zero-temperature Monte Carlo results.