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We investigate the dynamic structure factor of atomic Bose and Fermi gases inone-dimensional optical lattices at zero temperature. The focus is on thegeneric behaviour of S(k,omega) as function of filling and interaction strengthwith the aim of identifying possible experimental signatures for the differentquantum phase transitions. We employ the Hubbard or Bose-Hubbard model andsolve the eigenvalue problem of the Hamiltonian exactly for moderate latticesizes. This allows us to determine the dynamic structure factor and otherobservables directly in the phase transition regime, where approximationschemes are generally not applicable. We discuss the characteristic signaturesof the various quantum phases appearing in the dynamic structure factor andillustrate that the centroid of the strength distribution can be used toestimate the relevant excitation gaps. Employing sum rules, these quantitiescan be evaluated using ground state expectation values only. Importantdifferences between bosonic and fermionic systems are observed, e.g., regardingthe origin of the excitation gap in the Mott-insulator phase.Comment: 15 pages, 7 figure

Dynamic structure factor of ultracold Bose and Fermi gases in optical lattices