BEC-BCS Crossover of a Trapped Two-Component Fermi Gas with Unequal Masses

Abstract

We determine the energetically lowest lying states in the BEC-BCS crossover regime of s-wave interacting two-component Fermi gases under harmonic confinement by solving the many-body Schrodinger equation using two distinct approaches. Essentially exact basis set expansion techniques are applied to determine the energy spectrum of systems with N=4 fermions. Fixed-node diffusion Monte Carlo methods are applied to systems with up to N=20 fermions, and a discussion of different guiding functions used in the Monte Carlo approach to impose the proper symmetry of the fermionic system is presented. The energies are calculated as a function of the s-wave scattering length a_s for N=2-20 fermions and different mass ratios κof the two species. On the BEC and BCS sides, our energies agree with analytically-determined first-order correction terms. We extract the scattering length and the effective range of the dimer-dimer system up to κ= 20. Our energies for the strongly-interacting trapped system in the unitarity regime show no shell structure, and are well described by a simple expression, whose functional form can be derived using the local density approximation, with one or two parameters. The universal parameter ξfor the trapped system for various κis determined, and comparisons with results for the homogeneous system are presented.

11 pages, 6 figures, extended version

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• Heavy-Light Fermion Mixtures at Unitarity
• Effective Nonlinear Schrödinger Equations for Cigar-Shaped and Disk-Shaped Fermi Superfluids at Unitarity
• Collisional properties of weakly bound heteronuclear dimers
• Density Functional Theory for non-relativistic Fermions in the Unitarity Limit
• Shock waves in strongly interacting Fermi gas from time-dependent density functional calculations
• Dimer-dimer collisions at finite energies in two-component Fermi gases
• Unnuclear physics
• Chandrasekhar-Clogston limit and phase separation in Fermi mixtures at Unitarity
• Small mass- and trap-imbalanced two-component Fermi systems
• Stability of Inhomogeneous Multi-Component Fermi Gases
• Energy spectrum of a harmonically trapped two-atom system with spin-orbit coupling
• Universal behavior of a trapped Fermi superfluid in the BCS-unitarity crossover
• Universal dimer-dimer scattering in lattice effective field theory
• Vortex core states in superfluid Fermi-Fermi mixtures with unequal masses
• 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
• Self-binding of one-dimensional fermionic mixtures with zero-range interspecies attraction
• Paired fermionic superfluids with s- and p-wave interactions
• Molecular regimes in ultracold Fermi gases