Spin-imbalanced atomic Fermi gases in one dimension and the prospects for FFLO superconductivity

Growing expertise to engineer, manipulate and probe different analogs of condensed matter systems allows to probe properties of exotic pairing states such as the Fulde-Ferrell-Larkin- Ovchinnikov state. Inspired by ongoing experiments at Rice university, we are studying the pairing in spin-imbalanced ultracold atomic system of fermions in one dimension. Calculations are done using the Bethe Ansatz technique and the trap is incorporated into the solution via local density (Thomas-Fermi) approximation. The thermodynamic-Bethe-Ansatz equations are solved numerically and different density profiles (total-, spin- and entropy-densities) are calculated in the trap for different finite temperatures. A scheme to identify the phase diagram using total density profiles in the trap is proposed that would be immediately useful for experimentalists.