BEC-BCS Crossover in the Epsilon Expansion

Abstract

The epsilon expansion (expansion around four spacial dimensions) developed by Nishida and Son for a cold fermi gas with infinite scattering length is extended to finite scattering length to study the BEC-BCS crossover. A resummation of higher order logarithms and a suitable extension of fermion coupling in d-dimensions are developed in order to apply the theory in the BCS regime. The ratio between the chemical potential and the Fermi energy, mu/eF, is computed to next-to-leading order in the epsilon expansion as a function of eta=1/(a kF), where a is the scattering length and kF is the Fermi momentum in a non-interacting system. Near the unitarity limit eta->0, we found mu/eF=0.475-0.707 eta-0.5 eta^2. Near the BEC limit eta->infinity, mu/eF=0.062/eta - eta^2, while near the BCS limit eta->-infinity, mu/eF=1+0.707/eta. Overall good agreement with Quantum Monte Carlo results is found.

9 pages, 3 figures

References in corpus (2)

• Crossover from a molecular Bose-Einstein condensate to a degenerate Fermi gas
• Phase diagram of a cold polarized Fermi gas

Cited by in corpus (6)

• Particle-hole fluctuations in the BCS-BEC Crossover
• Renormalisation Flow and Universality for Ultracold Fermionic Atoms
• Dilute neutron matter on the lattice at next-to-leading order in chiral effective field theory
• Ground-state energy of the unitary Fermi gas from the epsilon expansion
• BCS BEC crossover and phase structure of relativistic system: a variational approach
• Low-momentum ring diagrams of neutron matter at and near the unitary limit