We present a study of the superfluid properties of atomic Bose gases inoptical lattice potentials using the Bose-Hubbard model. To do this, we use amicroscopic definition of the superfluid fraction based on the response of thesystem to a phase variation imposed by means of twisted boundary conditions. Wecompare the superfluid fraction to other physical quantities, i.e., theinterference pattern after ballistic expansion, the quasi-momentumdistribution, and number fluctuations. We have performed exact numericalcalculations of all these quantities for small one-dimensional systems. We showthat the superfluid fraction alone exhibits a clear signature of theMott-insulator transition. Observables like the fringe visibility, which probeonly ground state properties, do not provide direct information onsuperfluidity and the Mott-insulator transition.
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