  Quantum phases of ultracold bosons with repulsive interactions in lattices in
the presence of quenched disorder are investigated. The disorder is assumed to
be caused by the interaction of the bosons with impurity atoms having a large
effective mass. The system is described by the Bose-Hubbard Hamiltonian with
random on-site energies which have a discrete binary probability distribution.
The phase diagram at zero temperature is calculated using several methods like
a strong-coupling expansion, an exact numerical diagonalization, and a
Bose-Fermi mapping valid in the hard-core limit. It is shown that the
Mott-insulator phase exists for any strength of disorder in contrast to the
case of continuous probability distribution. We find that the compressibility
of the Bose glass phase varies in a wide range and can be extremely low.
Furthermore, we evaluate experimentally accessible quantities like the momentum
distribution, the static and dynamic structure factors, and the density of
excited states. The influence of finite temperature is discussed as well.
