Fulde-Ferrell-Larkin-Ovchinnikov states in a superfluid Fermi gas

Recently, both the experimental and theoretical studies to realize superfluid states in atomic gases have been performed by using a 50-50 mixture of atoms in two hyperfine spin states. We discuss favorable superfluid states in an unequal mixture. Such situation is analogous to a superconducting state in the presence of a magnetic field acting on the electron spins and then the natural candidate for the ground state is known as the Fulde-Ferrell-Larkin- Ovchinnikov (FFLO) state which is a spatially inhomogeneous superfluid state. We examine the possibility of the FFLO state in two species gas of Fermions confined in a realistic three-dimensional harmonic trap. We propose a clear experimental way to create and directly detect the spatially modulated FFLO state from the macroscopic signature.