Competition between normal superfluidity and Larkin-Ovchinnikov phases of polarized Fermi gases in elongated traps

By applying the recently proposed antisymmetric superfluid local density approximation (ASLDA) to strongly interacting polarized atomic gases at unitarity in very elongated traps, we find families of solutions of the Larkin-Ovchinnikov (LO) type with prominent transversal oscillation of the pairing potential. These LO states coexist with a superfluid state having a smooth pairing potential. We suggest that the LO phase could be accessible experimentally by increasing the trap aspect ratio adiabatically. We show that the local asymmetry effects contained in the ASLDA do not support a deformed superfluid core predicted by previous Bogoliubov–de Gennes treatments.