Abstract: In this paper, we discuss the search for the Fulde–Ferrell–Larkin–Ovchinnikov superfluid phase in an ultracold gas of Fermi atoms. A possible obstacle to obtaining this phase in known experiments is, first of all, the separation of the gas into a spin-balanced phase and a completely polarized phase. This phase separation is caused by confinement in an external parabolic potential. A second possible obstacle is the insufficiently low temperature-to-Fermi energy ratio. Trapping the gas in a large-scale optical-dipole trap with a flat potential inside will avoid phase separation. Moreover, the trap will allow an increase in the number of atoms, which, in turn, can lead to a decrease in the temperature relative to the Fermi energy. The results of a primary experiment on loading atoms into a similar trap from a magneto-optical trap are presented.