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

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