  We investigate the effect of the trapping potential on the quantum phases of
strongly correlated ultracold bosons in one-dimensional periodic and
quasiperiodic optical lattices. By means of a decoupling meanfield approach, we
characterize the ground state of the system and its behavior under variation of
the harmonic trapping, as a function of the total number of atoms. For a small
atom number the system shows an incompressible Mott-insulating phase, as the
size of the cloud remains unaffected when the trapping potential is varied.
When the quasiperiodic potential is added the system develops a
metastable-disordered phase which is neither compressible nor Mott insulating.
This state is characteristic of quasidisorder in the presence of a strong
trapping potential.
