Bogoliubov Excitations and Superfluidity in a Kronig-Penney Potential*

We study the elementary excitations of Bose-Einstein condensates in a Kronig-Penney potential. We solve the Bogoliubov equations analytically and obtain the band structure of the excitation spectrum. We show that the excitation spectrum is phononlike at low energies. It is found that the anomalous tunneling of low-energy excitations is crucial to the phonon dispersion, which is directly connected to the superfluidity of the condensate.