Spontaneous Vortices in Imbalance Populated Fermion Gas, Finite Size System

Atomic Fermion gases with mismatched densities have attracted much interest recently both experimentally and theoretically. These gases are related to superconductors in a magnetic field, to color superconductivity in high density QCD and to other systems. The main focus of recent research is on the possibility of unusual pairing states, the Larkin-Ovchinnikov-Fulde-Ferrel(LOFF)[1] phase, the Deformed Fermi surface(DFS)[2] and other states have been suggested in the past few years. We work specifically on two-dimensional systems with circular hard walls which contain atoms with two different hyperfine states and different populations. In addition to phase separation, a phenomenon that has already been observed[3], we consider the possibility of the spontaneous formation of vortices and giant vortices in some regions of parameter space. [1] Qinghong Cui, C.-R. Hu, J.Y.T. Wei, and Kun Yang, cond-mat/0510717 [2] A. Sedrakian et al.,cond-mat/0404577 [3] R. Hulet, preprint.