Natural and unnatural parity states of small trapped equal-mass two-component Fermi gases at unitarity and fourth-order virial coefficient

Authors:
  • DRD. Rakshit
    D. Rakshit
  • KDK. M. Daily
    K. M. Daily
  • DBD. Blume
    D. Blume
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Abstract
Equal-mass two-component Fermi gases under spherically symmetric external harmonic confinement with large s-wave scattering length are considered. Using the stochastic variational approach, we determine the lowest 286 and 164 relative eigenenergies of the (2,2) and (3,1) systems at unitarity as a function of the range r0 of the underlying two-body potential and extrapolate to the r0$\rightarrow${}0 limit. Our calculations include all states with vanishing and finite angular momentum L (and natural and unnatural parity $\Pi${}) with relative energy up to 10.5~$\hbar${}$\Omega${}, where $\Omega${} denotes the angular trapping frequency of the external confinement. Our extrapolated zero-range energies are estimated to have uncertainties of 0.1% or smaller. The (2,2) and (3,1) energies are used to determine the fourth-order virial coefficient of the trapped unitary two-component Fermi gas in the low-temperature regime. Our results are compared with recent predictions for the fourth-order virial coefficient of the homogeneous system. We also calculate small portions of the energy spectra of the (3,2) and (4,1) systems at unitarity.

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