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 (14)

• Observation of a Strongly-Interacting Degenerate Fermi Gas of Atoms
• Vortices and Superfluidity in a Strongly Interacting Fermi Gas
• Observation of the Pairing Gap in a Strongly Interacting Fermi Gas
• Experimental Study of the BEC-BCS Crossover Region in Lithium 6
• Crossover from a molecular Bose-Einstein condensate to a degenerate Fermi gas
• Superfluid Fermi Gases with Large Scattering Length
• Heat Capacity of a Strongly-Interacting Fermi Gas
• The unitary gas in an isotropic harmonic trap: symmetry properties and applications
• The potential energy of a ${}^{40}$K Fermi gas in the BCS-BEC crossover
• Local Density Approximation for Systems with Pairing Correlations
• Energy Density Functional Approach to Superfluid Nuclei
• Density-functional theory for fermions in the unitary regime
• Cooper pairing and single particle properties of trapped Fermi gases
• Shell structure and pairing for interacting fermions in a trap

Cited by in corpus (56)

• Nonrelativistic conformal field theories
• The BCS-BEC crossover: From ultra-cold Fermi gases to nuclear systems
• Universal few-body physics and cluster formation
• Applications of quantum Monte Carlo methods in condensed systems
• Few-body physics with ultracold atomic and molecular systems in traps
• Local Density Functional Theory for Superfluid Fermionic Systems: The Unitary Gas
• Comparing and contrasting nuclei and cold atomic gases
• Universal properties of a trapped two-component Fermi gas at unitarity
• Resonantly Interacting Fermions In a Box
• Cold neutrons trapped in external fields
• Superfluid Bose-Fermi mixture from weak-coupling to unitarity
• Extended Thomas-Fermi Density Functional for the Unitary Fermi Gas
• Energetics and Structural Properties of Trapped Two-Component Fermi Gases
• Quantum Monte Carlo approaches to nuclear and atomic physics
• BEC-BCS Crossover of a Trapped Two-Component Fermi Gas with Unequal Masses
• Thermodynamics of a Trapped Unitary Fermi Gas
• Effective-Range Dependence of Resonantly Interacting Fermions
• Lattice methods for strongly interacting many-body systems
• 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
• Self-trapping of a Fermi super-fluid in a double-well potential in the BEC-unitarity crossover
• Lattice Monte Carlo calculations for unitary fermions in a harmonic trap
• Correlated Gaussian Hyperspherical Method for Few-Body Systems
• Three and Four Harmonically Trapped Particles in an Effective Field Theory Framework
• Effective Nonlinear Schrödinger Equations for Cigar-Shaped and Disk-Shaped Fermi Superfluids at Unitarity
• Analytic Harmonic Approach to the N-body problem
• Density Functional Theory for non-relativistic Fermions in the Unitarity Limit
• A new effective interaction for the trapped Fermi gas
• Structure and dynamics of a rotating superfluid Bose-Fermi mixture
• Probing strongly interacting atomic gases with energetic atoms
• Unnuclear physics
• Universality of the unitary Fermi gas: A few-body perspective
• Trapped two-component Fermi gases with up to six particles: Energetics, structural properties, and molecular condensate fraction
• Universal scaling in a trapped Fermi super-fluid in the BCS-unitarity crossover
• Effective interactions for light nuclei: an effective (field theory) approach
• Energy and structural properties of $N$-boson clusters attached to three-body Efimov states: Two-body zero-range interactions and the role of the three-body regulator
• Small mass- and trap-imbalanced two-component Fermi systems
• Predicting Energies of Small Clusters from the Inhomogeneous Unitary Fermi Gas
• Shell-Model Monte Carlo Simulations of BCS-BEC Crossover in Few-Fermion Systems
• Trapped unitary two-component Fermi gases with up to ten particles
• Universal Two-Body Spectra of Ultracold Harmonically Trapped Atoms in Two and Three Dimensions
• Universal few-body physics in a harmonic trap
• BCS-BEC crossover in a trapped Fermi super-fluid using a density-functional equation
• Stability of Inhomogeneous Multi-Component Fermi Gases
• Configuration-interaction Monte Carlo method and its application to the trapped unitary Fermi gas
• Fermionic ground state at unitarity and Haldane Exclusion Statistics
• Universal behavior of a trapped Fermi superfluid in the BCS-unitarity crossover
• Effective interactions and operators in no-core shell model
• Second-Order Perturbation Theory in Continuum Quantum Monte Carlo Calculations
• Vortices in low-density neutron matter and cold Fermi gases
• Fate of Multiparticle Resonances: From $Q$-Balls to ${}^3$He Droplets
• Dynamical properties of the unitary Fermi gas: collective modes and shock waves
• Effective Lagrangian of unitary Fermi gas from $\epsilon$ expansion
• A new effective interaction for the trapped fermi gas: the BEC-BCS crossover
• On the kinetic energy of unitary Fermi gas in a harmonic trap
• Mapping the Two-Component Atomic Fermi Gas to the Nuclear Shell-Model