  The exotic Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states have been actively
searched for experimentally since the mean-field based FFLO theories were put
forward half a century ago. Here we investigate the stability of FFLO states
against unavoidable pairing fluctuations, and conclude that FFLO superfluids
cannot exist due to their intrinsic instability in three and two dimensions.
This explains their absence in experimental observations in both condensed
matter systems and the most recent, more promising ultracold atomic Fermi gases
with a population imbalance.
