Absence of fermionic quasi-particles in the superfluid state of the attractive Fermi gas

We calculate the effect of order parameter fluctuations on the fermionic single-particle excitations in the superfluid state of neutral fermions interacting with short range attractive forces. We show that in dimensions D \leq 3 the singular effective interaction between the fermions mediated by the gapless Bogoliubov-Anderson mode prohibits the existence of well-defined quasi-particles. We explicitly calculate the single-particle spectral function in the BEC regime in D=3 and show that in this case the quasi-particle residue and the density of states are logarithmically suppressed.