  A rotating ultracold S-wave superfluid Fermi gas is considered, when the
population imbalance (or equivalently the mismatch in chemical potentials)
corresponds to the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) state in the
vicinity of the Lifshitz critical point. It is shown that under these
conditions the critical angular velocity in two-dimensional systems is an
oscillating function of temperature and population imbalance giving rise to
reentrant superfluid phases. This leads to vortex lattices with
multiple-quantized circulation quanta. The reason for this behavior is the
population by Cooper pairs of the Landau levels above the lowest one.
