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We calculate the superfluid fraction of an interacting Fermi gas, in thepresence of a one-dimensional periodic potential of strength $V_0$ andwave-vector $q$. Special focus is given to the unitary Fermi gas, characterizedby the divergent behavior of the s-wave scattering length. Comparison with theLeggett's upper bound $(\langle n_{1D}\rangle <1/n_{1D}>)^{-1}$, with $n_{1D}$the 1D column density, explicitly shows that, differently from the case of adilute interacting Bose gas, the bound significantly overestimates the value ofthe superfluid fraction, except in the phonon regime of small $q$. Sum rulearguments show that the combined knowledge of the Leggett bound and of theactual value of the superfluid fraction allows for the determination ofcurvature effects providing the deviation of the dispersion of theAnderson-Bogoliubov mode from the linear phonon dependence. The comparison withthe predictions of the weakly interacting BCS Fermi gas points out the crucialrole of two-body interactions. The implications of our predictions on theanisotropic behavior of the sound velocity are also discussed.

Superfluid Fraction and Leggett Bound in a Density Modulated Strongly Interacting Fermi Gas at Zero Temperature