2006/10/01 by Jiunn-Wei Chen, Eiji Nakano · 2 citations
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Physics of Superconductivity and Magnetism #Quantum, superfluid, helium dynamics #cond-mat.other #hep-lat #hep-ph #nucl-th
paper · pdf · doi:10.1103/physreva.75.043620
published as Phys.Rev.A75:043620,2007 · 9 pages, 3 figures
arxiv created 2006/10/01 · openalex publication_date 2007/04/23 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The ϵ 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, \ensuremathμ∕\ensuremathεF, is computed to next-to-leading order in the ϵ expansion as a function of \ensuremathη=1∕(akF), where a is the scattering length and kF is the Fermi momentum in a noninteracting system. Near the unitarity limit \ensuremath|\ensuremathη\ensuremath|\ensuremath→0, we found \ensuremathμ∕\ensuremathεF=0.475\ensuremath-0.707\ensuremathη\ensuremath-0.5\ensuremathη2. Near the BEC limit \ensuremathη\ensuremath→\ensuremath∞, \ensuremathμ∕\ensuremathεF=0.062∕\ensuremathη\ensuremath-\ensuremathη2, while near the BCS limit \ensuremathη\ensuremath→\ensuremath-\ensuremath∞, \ensuremathμ∕\ensuremathεF=1+0.707∕\ensuremathη. Overall good agreement with quantum Monte Carlo results is found.