Pairing in a two-component ultracold Fermi gas: phases with broken space symmetries

TL;DR

This paper investigates the phase diagram of a two-component ultracold Fermi gas, revealing a transition from BCS to phases with broken space symmetries, including deformed Fermi surface superfluidity, with potential experimental detection.

Contribution

It introduces and analyzes the deformed Fermi surface superfluidity phase in asymmetric ultracold Fermi gases, comparing it to the LOFF phase and discussing experimental detection methods.

Findings

DFS phase lowers condensation energy in asymmetric conditions

Critical asymmetries for DFS are larger than for BCS

Potential detection of DFS in $^6$Li experiments

Abstract

We explore the phase diagram of a two-component ultracold atomic Fermi gas interacting with zero-range forces in the limit of weak-coupling. We focus on the dependence of the pairing gap and the free energy on the variations in the number densities of the two species while the total density of the system is held fixed. As the density asymmetry is increased, the system exhibits a transition from a homogenous Bardeen-Cooper-Schrieffer (BCS) phase to phases with spontaneously broken global space symmetries. One such realization is the deformed Fermi surface superfluidity (DFS) which exploits the possibility of deforming the Fermi-surfaces of the species into ellipsoidal form at zero total momentum of Cooper pairs. The critical asymmetries at which the transition from the DFS to the unpaired state occurs are larger than those for the BCS phase. In this precritical region the DFS phase lowers the condensation energy of the asymmetric BCS state. We compare quantitatively the DFS phase to another realization of superconducting phases with broken translational symmetry - the single plane wave Larkin-Ovchinnikov-Fulde-Ferrell (LOFF)phase, which is characterized by a non-vanishing center-of-mass momentum of the Cooper pairs. The possibility of the detection of the DFS phase in the time-of-flight experiments is discussed and quantified for the case of $^6$Li atoms trapped in two different hyperfine states.