Instability of Fulde-Ferrell-Larkin-Ovchinnikov states in three and two dimensions

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.