  Spin-imbalanced ultracold Fermi gases have been widely studied recently as a
platform for exploring the long-sought Fulde-Ferrell-Larkin-Ovchinnikov
superfluid phases, but so far conclusive evidence has not been found. Here we
propose to realize an Fulde-Ferrell (FF) superfluid without spin imbalance in a
three-dimensional fermionic cold atom optical lattice, where $s$- and
$p$-orbital bands of the lattice are coupled by another weak moving optical
lattice. Such coupling leads to a spin-independent asymmetric Fermi surface,
which, together with the $s$-wave scattering interaction between two spins,
yields an FF type of superfluid pairing. Unlike traditional schemes, our
proposal does not rely on the spin imbalance (or an equivalent Zeeman field) to
induce the Fermi surface mismatch and provides a completely new route for
realizing FF superfluids.
