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arXiv:1111.5079 · Physical Review A

Equation of state of the unitary Fermi gas: An update on lattice calculations

Joaquín E. Drut, Timo A. Lähde, Gabriel Wlazłowski, Piotr Magierski

Published May 1, 2012• 41 citations
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Abstract

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.

DOI
10.1103/physreva.85.051601

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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.

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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/\ensuremathϵF\ensuremath≃0.20T/{\ensuremath{\epsilon}}_{F}^{}\ensuremath{\simeq}0.20T/\ensuremathϵF​\ensuremath≃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.
The unitary Fermi gas (UFG) is a strongly correlated system of two-species (spin-1/2) fermions with a short-range attractive interaction modeled by a contact interaction and has attracted much interest across different disciplines. The UFG is considered a paradigm for strongly correlated superfluids and has been investigated extensively, with generally good agreement found between theory and experiment. However, the extent of a pseudogap regime above the critical temperature TcT_cTc​ for superfluidity is still debated both theoretically and experimentally. Here we study thermodynamic properties of the UFG across the superfluid phase transition using finite-temperature lattice auxiliary-field quantum Monte Carlo (AFMC) methods in the canonical ensemble of fixed particle numbers. We extrapolate our lattice AFMC results to the continuous time and continuum limits, thus removing the systematic error associated with the finite filling factor of previous AFMC studies. We determine the critical temperature to be Tc=0.16(1) TFT_c=0.16(1)\, T_{F}Tc​=0.16(1)TF​. For the largest particle number studied N=114N=114N=114, the energy-staggering pairing gap is suppressed above a pairing scale temperature of T∗≈0.2 TFT^{*}\approx 0.2\,T_FT∗≈0.2TF​. The spin susceptibility displays moderate suppression above TcT_cTc​ with a spin gap temperature of Ts≈0.2 TFT_s\approx 0.2 \,T_FTs​≈0.2TF​. We also calculate a free energy-staggering pairing gap, which shows substantially reduced statistical errors when compared with the energy-staggering gap, allowing for a clear signature of pairing correlations in the finite-size system. All results indicate that the pseudogap regime is narrow, with pseudogap signatures emerging at temperatures below T∗≈0.2 TFT^{*}\approx 0.2 \, T_FT∗≈0.2TF​. The reduced statistical errors of the free energy gap enable an extrapolation at low temperatures, allowing an estimate of the zero-temperature pairing gap ΔE=0.576(24) εFΔ_E = 0.576(24) \, ε_FΔE​=0.576(24)εF​.
The Unitary Fermi Gas (UFG) is one of the most strongly interacting systems known to date, as it saturates the unitarity bound on the quantum mechanical scattering cross section. The UFG corresponds to a two-component Fermi gas in the limit of short interaction range and large scattering length, and is currently realized in ultracold-atom experiments via Feshbach resonances. While easy to define, the UFG poses a challenging quantum many-body problem, as it lacks any characteristic scale other than the density. As a consequence, accurate quantitative predictions of the thermodynamic properties of the UFG require Monte Carlo calculations. However, significant progress has also been made with purely analytical methods. Notably, in 2005 Tan derived a set of exact thermodynamic relations in which a universal quantity known as the "contact" C plays a crucial role. Recently, C has also been found to determine the prefactor of the high- frequency power-law decay of correlators as well as the right-hand-sides of shear- and bulk viscosity sum rules. The contact is therefore a central piece of information on the UFG in equilibrium as well as away from equilibrium. In this talk we describe some of the known aspects of Fermi gases at and around unitarity, show our latest Monte Carlo results for the contact at finite temperature, and summarize the open questions in the field, some of which we are starting to answer using large-scale Monte Carlo calculations by adapting methods from Lattice QCD.
The Unitary Fermi Gas (UFG) is one of the most strongly interacting systems known to date, as it saturates the unitarity bound on the quantum mechanical scattering cross section.The UFG corresponds to a two-component Fermi gas in the limit of short interaction range and large scattering length, and is currently realized in ultracold-atom experiments via Feshbach resonances.While easy to define, the UFG poses a challenging quantum many-body problem, as it lacks any characteristic scale other than the density.As a consequence, accurate quantitative predictions of the thermodynamic properties of the UFG require Monte Carlo calculations.However, significant progress has also been made with purely analytical methods.Notably, in 2005 Tan derived a set of exact thermodynamic relations in which a universal quantity known as the "contact" C plays a crucial role.Recently, C has also been found to determine the prefactor of the high-frequency power-law decay of correlators as well as the right-hand-sides of shear-and bulk viscosity sum rules.The contact is therefore a central piece of information on the UFG in equilibrium as well as away from equilibrium.In this talk we describe some of the known aspects of Fermi gases at and around unitarity, show our latest Monte Carlo results for the contact at finite temperature, and summarize the open questions in the field, some of which we are starting to answer using large-scale Monte Carlo calculations by adapting methods from Lattice QCD.
The Unitary Fermi Gas (UFG) is one of the most strongly interacting systems known to date, as it saturates the unitarity bound on the quantum mechanical scattering cross section. The UFG corresponds to a two-component Fermi gas in the limit of short interaction range and large scattering length, and is currently realized in ultracold-atom experiments via Feshbach resonances. While easy to define, the UFG poses a challenging quantum many-body problem, as it lacks any characteristic scale other than the density. As a consequence, accurate quantitative predictions of the thermodynamic properties of the UFG require Monte Carlo calculations. However, significant progress has also been made with purely analytical methods. Notably, in 2005 Tan derived a set of exact thermodynamic relations in which a universal quantity known as the "contact" C plays a crucial role. Recently, C has also been found to determine the prefactor of the high- frequency power-law decay of correlators as well as the right-hand-sides of shear- and bulk viscosity sum rules. The contact is therefore a central piece of information on the UFG in equilibrium as well as away from equilibrium. In this talk we describe some of the known aspects of Fermi gases at and around unitarity, show our latest Monte Carlo results for the contact at finite temperature, and summarize the open questions in the field, some of which we are starting to answer using large-scale Monte Carlo calculations by adapting methods from Lattice QCD.
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.