We consider mass-imbalanced two-component Fermi gases for which the unequal-mass atoms interact via a zero-range model potential with a diverging $s$ -wave scattering length ${a}_{s}$ , that is, with $1/{a}_{s}=0$ . The high-temperature thermodynamics of the harmonically trapped and homogeneous systems are examined using a virial expansion approach up to third order in the fugacity. We find that the universal part of the third-order virial coefficient associated with two light atoms and one heavy atom is negative, while that associated with two heavy and one light atom changes sign from negative to positive as the mass ratio $\ensuremath{\kappa}$ increases and diverges when Efimov physics sets in at $\ensuremath{\kappa}=13.61$. By examining the Helmholtz free energy, we find that the equilibrium polarization of the trapped and homogeneous systems is 0 for $\ensuremath{\kappa}=1$, but finite for $\ensuremath{\kappa}\ensuremath{\ne}1$ (with a majority of heavy particles). Compared to the equilibrium polarization of the noninteracting system, the equilibrium polarization at unitarity is increased for the trapped system and decreased for the homogeneous system. We find that unequal-mass Fermi gases are stable for all polarizations.We consider mass-imbalanced two-component Fermi gases for which the unequal-mass atoms interact via a zero-range model potential with a diverging $s$-wave scattering length ${a}_{s}$, that is, with $1/{a}_{s}=0$. The high-temperature thermodynamics of the harmonically trapped and homogeneous systems are examined using a virial expansion approach up to third order in the fugacity. We find that the universal part of the third-order virial coefficient associated with two light atoms and one heavy atom is negative, while that associated with two heavy and one light atom changes sign from negative to positive as the mass ratio $\ensuremath{\kappa}$ increases and diverges when Efimov physics sets in at $\ensuremath{\kappa}=13.61$. By examining the Helmholtz free energy, we find that the equilibrium polarization of the trapped and homogeneous systems is 0 for $\ensuremath{\kappa}=1$, but finite for $\ensuremath{\kappa}\ensuremath{\ne}1$ (with a majority of heavy particles). Compared to the equilibrium polarization of the noninteracting system, the equilibrium polarization at unitarity is increased for the trapped system and decreased for the homogeneous system. We find that unequal-mass Fermi gases are stable for all polarizations.

arXiv:1110.1400Physical Review AJan 5, 201231 citations

Theory of strongly interacting Fermi gases

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

Ultra-cold atomic Fermi gases at nano-Kelvin temperatures provide a new paradigm for the foundations of quantum many-body theory. Here, we summarize our recent theoretical efforts to understand the intriguing properties of these strongly correlated Fermi gases. A number of powerful theoretical techniques have been developed, including (i) a quantitative diagrammatic theory taken to infinite order; (ii) a virial expansion at high temperature; (iii) exact solutions for one-dimensional many-body systems; and (iv) new quantum simulations using the Gaussian Fermi representation. We have employed these techniques to predict universal thermodynamics in the strongly interacting limit and exotic quantum superfluid phases with imbalanced spin populations. More insights into strongly interacting Fermi gases are anticipated, by extending the Gaussian Fermi simulations to new regimes.Ultra-cold atomic Fermi gases at nano-Kelvin temperatures provide a new paradigm for the foundations of quantum many-body theory. Here, we summarize our recent theoretical efforts to understand the intriguing properties of these strongly correlated Fermi gases. A number of powerful theoretical techniques have been developed, including (i) a quantitative diagrammatic theory taken to infinite order; (ii) a virial expansion at high temperature; (iii) exact solutions for one-dimensional many-body systems; and (iv) new quantum simulations using the Gaussian Fermi representation. We have employed these techniques to predict universal thermodynamics in the strongly interacting limit and exotic quantum superfluid phases with imbalanced spin populations. More insights into strongly interacting Fermi gases are anticipated, by extending the Gaussian Fermi simulations to new regimes.

Journal of Modern OpticsAug 14, 20092 citations

Strongly interacting polarized Fermi gas in one dimension

Xia-Ji Liu, Hui Hu, Shiqun Li

Jan 1, 20070 citations

We consider mass-imbalanced two-component Fermi gases for which the unequal-mass atoms interact via a zero-range model potential with a diverging

s

-wave scattering length

{a}_{s}

, that is, with

1/{a}_{s}=0

. The high-temperature thermodynamics of the harmonically trapped and homogeneous systems are examined using a virial expansion approach up to third order in the fugacity. We find that the universal part of the third-order virial coefficient associated with two light atoms and one heavy atom is negative, while that associated with two heavy and one light atom changes sign from negative to positive as the mass ratio $\ensuremath{\kappa}$ increases and diverges when Efimov physics sets in at $\ensuremath{\kappa}=13.61$. By examining the Helmholtz free energy, we find that the equilibrium polarization of the trapped and homogeneous systems is 0 for $\ensuremath{\kappa}=1$, but finite for $\ensuremath{\kappa}\ensuremath{\ne}1$ (with a majority of heavy particles). Compared to the equilibrium polarization of the noninteracting system, the equilibrium polarization at unitarity is increased for the trapped system and decreased for the homogeneous system. We find that unequal-mass Fermi gases are stable for all polarizations.