BEC-BCS Crossover in the Epsilon Expansion
Journal
Physical Review
Journal Volume
A75
Pages
043620
Date Issued
2006-10
Author(s)
Abstract
The expansion (expansion around four spatial dimensions) developed by Nishida and Son for a cold Fermi gas with infinite scattering length is extended to finite scattering length to study the Bose-Einstein condensate (BEC) to 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, μ εF, is computed to next-to-leading order in the expansion as a function of η=1(a kF), where a is the scattering length and kF is the Fermi momentum in a noninteracting system. Near the unitarity limit η→0, we found μ εF =0.475-0.707η-0.5 η2. Near the BEC limit η→, μ εF =0.062η- η2, while near the BCS limit η→-, μ εF =1+0.707η. Overall good agreement with quantum Monte Carlo results is found. © 2007 The American Physical Society.
SDGs
Type
journal article