Recent ground-breaking experiments studying the effects of spin polarization on pairing in unitary Fermi gases encountered mutual qualitative and quantitative discrepancies which seem to be a function of the confining geometry. Using numerical algorithms we study the solution space for a three-dimensional fully self-consistent formulation of realistic systems with up to
105 atoms. A study of the three types of solutions obtained demonstrates a tendency toward metastability as the confining geometry is elongated. One of these solutions, which is consistent with Rice experiments at high trap aspect ratio, supports a state strikingly similar to the long sought Fulde-Ferrel-Larkin-Ovchinnikov state. Our study helps to resolve the long-standing controversy concerning the discrepancies between the findings from two different experimental groups and highlights the versatility of actual-size numerical calculations for investigating inhomogeneous fermionic superfluids.
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.