  Larkin-Ovchinnikov (LO) state which combines the superfluidity and spatial
periodicity of pairing order parameter and exhibits the supersolid properties
has been attracting intense attention in both condensed matter physics and
ultracold atoms. Conventionally, realization of LO state from an intrinsic
s-wave interacting system necessitates to break the time-reversal (TR) and
sometimes spatial-inversion (SI) symmetries. Here we report a novel prediction
that the LO state can be realized in a TR and SI symmetric system representing
a bilayer Fermi gas subjected to a laserassisted interlayer tunneling. We show
that the intralayer s-wave atomic interaction acts effectively like a p-wave
interaction in the pseudospin space. This provides distinctive pairing effects
in the present system with pseudspin spin-orbit coupling, and leads to a
spontaneous density-modulation of the pairing order predicted in a very broad
parameter regime. Unlike the conventional schemes, our results do not rely on
the spin imbalance or external Zeeman fields, showing a highly feasible way to
observe the long-sought-after LO superfluid phase using the laser-assisted
bilayer Fermi gases.
