  We propose a simple approach to realize two-dimensional Floquet topological
superfluid by periodically tuning the depth of square optical lattice
potentials. We show that the periodic driving can induce topological phase
transitions between trivial superfluid and Floquet topological superfluid. For
this systems we verify the anomalous bulk-boundary correspondence, namely that
the robust chiral Floquet edge states can appear even when the winding number
of all the bulk Floquet bands is zero. We establish the existence of two
Floquet Majorana zero modes separated in the quasienergy space, with
$\varepsilon_{0,\pi}=0,\pi/T$ at the topological defects.

Quantum Gases