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We study theoretically the superfluidity and stability of a Bose-Einsteincondensate (BEC) whose interatomic scattering length is periodically modulatedwith optical Feshbach resonance. Our numerical study finds that the propertiesof this periodic BEC are strongly influenced by the modulation strength. Whenthe modulation strength is small, only the Bloch waves close to the Brillouinzone edge suffer both Landau and dynamical instabilities. When the modulationstrength is strong enough, all Bloch waves become dynamically unstable. Inother words, the periodic BEC loses its superfluidity completely.

Superfluidity and Stabilities of a Bose-Einstein condensate with periodically modulated interatomic interaction