  We study theoretically the low-temperature phases of a two-component atomic
Fermi gas with attractive s-wave interactions under conditions of rapid
rotation. We find that, in the extreme quantum limit, when all particles occupy
the lowest Landau level, the normal state is unstable to the formation of
"charge" density wave (CDW) order. At lower rotation rates, when many Landau
levels are occupied, we show that the low-temperature phases can be
supersolids, involving both CDW and superconducting order.
