Unitary Fermi Gas in a Harmonic Trap

Abstract

We present an {\it ab initio} calculation of small numbers of trapped, strongly interacting fermions using the Green's Function Monte Carlo method (GFMC). The ground state energy, density profile and pairing gap are calculated for particle numbers $N=2\sim 22$ using the parameter-free "unitary" interaction. Trial wave functions are taken of the form of correlated pairs in a harmonic oscillator basis. We find that the lowest energies are obtained with a minimum explicit pair correlation beyond that needed to exploit the degeneracy of oscillator states. We find that energies can be well fitted by the expression $a_{TF}{E}_{TF}+\Delta \mathrm{mod}(N,2)$ where $E_{TF}$ is the Thomas-Fermi energy of a noninteracting gas in the trap and $\Delta$ is a pairing gap. There is no evidence of a shell correction energy in the systematics, but the density distributions show pronounced shell effects. We find the value $\Delta =0.7\pm 0.2\omega$ for the pairing gap. This is smaller than the value found for the uniform gas at a density corresponding to the central density of the trapped gas.

2 figures, 2 tables

References in corpus (4)

• Vortices and Superfluidity in a Strongly Interacting Fermi Gas
• Observation of the Pairing Gap in a Strongly Interacting Fermi Gas
• Crossover from a molecular Bose-Einstein condensate to a degenerate Fermi gas
• Density-functional theory for fermions in the unitary regime

Cited by in corpus (8)

• Nonrelativistic conformal field theories
• Local Density Functional Theory for Superfluid Fermionic Systems: The Unitary Gas
• Thermodynamics of a Trapped Unitary Fermi Gas
• Large Amplitude Dynamics of the Pairing Correlations in a Unitary Fermi Gas
• Level crossing in the three-body problem for strongly interacting fermions in a harmonic trap
• Density Functional Theory for non-relativistic Fermions in the Unitarity Limit
• Shell-Model Monte Carlo Simulations of BCS-BEC Crossover in Few-Fermion Systems
• Stability of Inhomogeneous Multi-Component Fermi Gases