  We present a study of the superfluid properties of atomic Bose gases in
optical lattice potentials using the Bose-Hubbard model. To do this, we use a
microscopic definition of the superfluid fraction based on the response of the
system to a phase variation imposed by means of twisted boundary conditions. We
compare the superfluid fraction to other physical quantities, i.e., the
interference pattern after ballistic expansion, the quasi-momentum
distribution, and number fluctuations. We have performed exact numerical
calculations of all these quantities for small one-dimensional systems. We show
that the superfluid fraction alone exhibits a clear signature of the
Mott-insulator transition. Observables like the fringe visibility, which probe
only ground state properties, do not provide direct information on
superfluidity and the Mott-insulator transition.
