Motivated by the prospect of optical lattice experiments with two-component Fermi gases consisting of different atomic species such as Li and K, we calculate the energies for $N$ fermions under harmonic confinement as a function of the mass and trap imbalance, i.e., as a function of the ratio between the masses and frequencies of species one and two, using microscopic approaches. Our energies for $N=2\ensuremath{-}6$ can be used to determine the energetically most favorable configuration for a given number of atoms per species of a deep lattice in which each lattice site is approximately harmonic and in which tunneling between neighboring sites can be neglected. We also determine and interpret the excitation gap for unequal-mass systems with up to $N=13$ atoms for equal oscillator lengths.Motivated by the prospect of optical lattice experiments with two-component Fermi gases consisting of different atomic species such as Li and K, we calculate the energies for $N$ fermions under harmonic confinement as a function of the mass and trap imbalance, i.e., as a function of the ratio between the masses and frequencies of species one and two, using microscopic approaches. Our energies for $N=2\ensuremath{-}6$ can be used to determine the energetically most favorable configuration for a given number of atoms per species of a deep lattice in which each lattice site is approximately harmonic and in which tunneling between neighboring sites can be neglected. We also determine and interpret the excitation gap for unequal-mass systems with up to $N=13$ atoms for equal oscillator lengths.

arXiv:0803.4221Physical Review AJul 10, 200824 citations

Thermodynamics of the two-component Fermi gas with unequal masses at unitarity

K. M. Daily, D. Blume

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

Motivated by the prospect of optical lattice experiments with two-component Fermi gases consisting of different atomic species such as Li and K, we calculate the energies for

N

fermions under harmonic confinement as a function of the mass and trap imbalance, i.e., as a function of the ratio between the masses and frequencies of species one and two, using microscopic approaches. Our energies for $N=2\ensuremath{-}6$ can be used to determine the energetically most favorable configuration for a given number of atoms per species of a deep lattice in which each lattice site is approximately harmonic and in which tunneling between neighboring sites can be neglected. We also determine and interpret the excitation gap for unequal-mass systems with up to

N=13

atoms for equal oscillator lengths.

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.