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arXiv:cond-mat/0701786 · Physical Review Letters

Thermodynamics of a Trapped Unitary Fermi Gas

Aurel Bulgac, Joaquín E. Drut, Piotr Magierski

Published Sep 18, 2007• 70 citations
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Abstract

We present the first model-independent comparison of recent measurements of the entropy and of the critical temperature of a unitary Fermi gas, performed by Luo et al., with the most complete results currently available from finite temperature Monte Carlo calculations. The measurement of the critical temperature in a cold fermionic atomic cloud is consistent with a value T(c) = 0.23(2)epsilon(F) in the bulk, as predicted by the present authors in their Monte Carlo calculations.

DOI
10.1103/physrevlett.99.120401

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We present the first model-independent comparison of recent measurements of the entropy and of the critical temperature of a unitary Fermi gas, performed by Luo et al., with the most complete results currently available from finite temperature Monte Carlo calculations. The measurement of the critical temperature in a cold fermionic atomic cloud is consistent with a value T(c) = 0.23(2)epsilon(F) in the bulk, as predicted by the present authors in their Monte Carlo calculations.
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We simulate the dilute attractive Fermi–Hubbard model in the unitarity regime using a diagrammatic determinant Monte Carlo (MC) algorithm with worm-type updates. We obtain the dependence of the critical temperature on the filling factor ν and, by extrapolating to ν → 0, determine the universal critical temperature of the continuum unitary Fermi gas in units of Fermi energy: T c /ε F = 0.152(7). We also determine the thermodynamic functions and show how the MC results can be used for accurate thermometry of a trapped unitary gas.
We report a model-independent measurement of the entropy, energy, and critical temperature of a degenerate, strongly interacting Fermi gas of atoms. The total energy is determined from the mean square cloud size in the strongly interacting regime, where the gas exhibits universal behavior. The entropy is measured by sweeping a bias magnetic field to adiabatically tune the gas from the strongly interacting regime to a weakly interacting regime, where the entropy is known from the cloud size after the sweep. The dependence of the entropy on the total energy quantitatively tests predictions of the finite-temperature thermodynamics.
We simulate the dilute attractive Fermi-Hubbard model in the unitarity regime using a diagrammatic determinant Monte Carlo algorithm with worm-type updates. We obtain the dependence of the critical temperature on the filling factor ννν and, by extrapolating to ν→0ν\to 0ν→0, determine the universal critical temperature of the continuum unitary Fermi gas in units of Fermi energy: Tc/εF=0.152(7)T_c/ε_F=0.152(7)Tc​/εF​=0.152(7). We also determine the thermodynamic functions and show how the Monte Carlo results can be used for accurate thermometry of a trapped unitary gas.
The thermodynamic properties of the unitary Fermi gas (UFG) have recently been measured to unprecedented accuracy at the MIT. In particular, these measurements provide an improved understanding of the regime below $T/{\ensuremath{\epsilon}}_{F}^{}\ensuremath{\simeq}0.20$, where a transition into a superfluid phase occurs. In light of this development, we present an overview of state-of-the-art auxiliary field quantum Monte Carlo (AFQMC) results for the UFG at finite temperature and compare them with the MIT data for the energy, chemical potential, and density. These AFQMC results have been obtained using methods based on the hybrid Monte Carlo (HMC) algorithm, which was first introduced within the context of lattice QCD.
Thermodynamic properties of an ultracold Fermi gas in a harmonic trap are calculated within a local density approximation, using a conserving many-body formalism for the BCS to Bose-Einstein condensate crossover problem, which has been developed by Haussmann et al. [Phys. Rev. A 75, 023610 (2007)]. We focus on the unitary regime near a Feshbach resonance and determine the local density and entropy profiles and the global entropy S(E)S(E)S(E) as a function of the total energy EEE. Our results are in good agreement with both experimental data and previous analytical and numerical results for the thermodynamics of the unitary Fermi gas. The value of the Bertsch parameter at T=0T=0T=0 and the superfluid transition temperature, however, differ appreciably. We show that, well in the superfluid regime, removal of atoms near the cloud edge enables cooling far below temperatures that have been reached so far.