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arXiv:1206.0237 · Physical Review A

Thermodynamic properties of universal Fermi gases

Erik M. Weiler, Theja N. De Silva

Published Jan 2, 2013• 2 citations
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Abstract

We develop a simple, mean-field-like theory for the normal phase of a unitary Fermi gas by deriving a self-consistent equation for its self-energy via a momentum-dependent coupling constant for both attractive and repulsive universal fermions. For attractive universal fermions in the lower branch of a Feshbach resonance, we use zero-temperature Monte Carlo results as a starting point for one-step iteration in order to derive an analytical expression for the momentum-dependent self-energy. For repulsive universal fermions in the upper branch of a Feshbach resonance, we iteratively calculate the momentum-dependent self-energy via our self-consistent equation. Lastly, for the case of population imbalance, we propose an ansatz for higher-order virial expansion coefficents. Overall, we find that our theory is in good agreement with currently available, high-temperature experimental data.

DOI
10.1103/physreva.87.013602

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We develop a simple, mean-field-like theory for the normal phase of a unitary Fermi gas by deriving a self-consistent equation for its self-energy via a momentum-dependent coupling constant for both attractive and repulsive universal fermions. For attractive universal fermions in the lower branch of a Feshbach resonance, we use zero-temperature Monte Carlo results as a starting point for one-step iteration in order to derive an analytical expression for the momentum-dependent self-energy. For repulsive universal fermions in the upper branch of a Feshbach resonance, we iteratively calculate the momentum-dependent self-energy via our self-consistent equation. Lastly, for the case of population imbalance, we propose an ansatz for higher-order virial expansion coefficents. Overall, we find that our theory is in good agreement with currently available, high-temperature experimental data.
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Exactly solvable models of ultracold Fermi gases are reviewed via their thermodynamic Bethe ansatz solution. Analytical and numerical results are obtained for the thermodynamics and ground state properties of two- and three-component one-dimensional attractive fermions with population imbalance. New results for the universal finite temperature corrections are given for the two-component model. For the three-component model, numerical solution of the dressed energy equations confirms that the analytical expressions for the critical fields and the resulting phase diagrams at zero temperature are highly accurate in the strong coupling regime. The results provide a precise description of the quantum phases and universal thermodynamics which are applicable to experiments with cold fermionic atoms confined to one-dimensional tubes.
Exactly solvable models of ultracold Fermi gases are reviewed via their thermodynamic Bethe Ansatz solution. Analytical and numerical results are obtained for the thermodynamics and ground state properties of two- and three-component one-dimensional attractive fermions with population imbalance. New results for the universal finite temperature corrections are given for the two-component model. For the three-component model, numerical solution of the dressed energy equations confirm that the analytical expressions for the critical fields and the resulting phase diagrams at zero temperature are highly accurate in the strong coupling regime. The results provide a precise description of the quantum phases and universal thermodynamics which are applicable to experiments with cold fermionic atoms confined to one-dimensional tubes.
We combine a Tan's universal relation with a basic statistical mechanical approach to derive a general equation of state for unitary Fermi gases. The universal equation of state is written as a series solution to a self consistent integral equation where the general solution is a linear combination of Fermi functions. By truncating our series solution to four terms with already known exact theoretical inputs at limiting cases, namely the first three virial coefficients and the Bertsch parameter, we find a good agreement with experimental measurements in the entire temperature region in the normal state. Our analytical equation of state agrees with experimental data up to the fugacity z=18z = 18z=18, which is a vast improvement over the other analytical equations of state available where the agreements is \emph{only} up to z≈7z \approx 7z≈7.
Quantum virial expansion provides an ideal tool to investigate the high-temperature properties of a strongly correlated Fermi gas. Here, we construct the virial expansion in the presence of spin-population imbalance. Up to the third order, we calculate the high-temperature free energy of a unitary Fermi gas as a function of spin imbalance, with infinitely large attractive or repulsive interactions. In the latter repulsive case, we show that there is no itinerant ferromagnetism when quantum virial expansion is applicable. We therefore estimate an upper bound for the ferromagnetic transition temperature Tc{T}_{c}Tc​. For a harmonically trapped Fermi gas at unitarity, we find that (Tc)upper<TF({T}_{c}){}_{\mathrm{upper}}<{T}_{F}(Tc​)upper​<TF​, where TF{T}_{F}TF​ is the Fermi temperature at the center of the trap. Our result for the high-temperature equations of state may confront future high-precision thermodynamic measurements.
We study the attractive and repulsive two-component Fermi gas with spin imbalance in two dimensions. Using a generalized TTT-matrix approximation, we examine the thermodynamic properties of both attractive and repulsive contact interacting Fermi gases. The interaction strength, which is characterized by the bound state energy Eb=ℏ2/ma2d2E_b=\hbar^2/m a_{2d}^2Eb​=ℏ2/ma2d2​ in vacuum, can be adjusted through a Feshbach resonance. We calculate the interaction energy, compressibility and spin susceptibility of the two branches of the Fermi gas. For the repulsive branch, we also find a critical strength of interaction a2d(c)a_{2d}^{(c)}a2d(c)​ above which this metastable thermodynamic state becomes unstable. This critical value depends on the temperature and the spin imbalance (the "magnetization") of the system.