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

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• Ultracold atoms and the Functional Renormalization Group
• Pseudogaps in strongly interacting Fermi gases
• Functional renormalization group approach to the BCS-BEC crossover
• Renormalisation Flow and Universality for Ultracold Fermionic Atoms
• Phase structure of spin-imbalanced unitary Fermi gases
• Modified Fermi-sphere, pairing gap and critical temperature for the BCS-BEC crossover
• From Low-Density Neutron Matter to the Unitary Limit
• Dilute neutron matter on the lattice at next-to-leading order in chiral effective field theory
• Precision benchmark calculations for four particles at unitarity
• The symmetric heavy-light ansatz
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• Strongly interacting Fermi systems in 1/N expansion: From cold atoms to color superconductivity
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• Finite-size and Particle-number Effects in an Ultracold Fermi Gas at Unitarity
• Low-momentum ring diagrams of neutron matter at and near the unitary limit
• Unitarity potentials and neutron matter at the unitary limit
• The Operator Product Expansion Beyond Leading Order for Two-Component Fermions
• An Effective Series Expansion to the Equation of State of Unitary Fermi Gases