  The phenomenon of Many-Body Stark Localization of bosons in tilted optical
lattice is studied. Despite the fact that no disorder is necessary for Stark
localization to occur, it is very similar to well known many body localization
(MBL) in sufficiently strong disorder. Not only the mean gap ratio reaches
poissonian value as characteristic for localized situations but also the
eigenstates reveal multifractal character as in standard MBL. Stark
localization enables a coexistence of spacially separated thermal and localized
phases in the harmonic trap similarly to fermions. Stark localization may also
lead to spectacular trapping of particles in a reversed harmonic field which
naively might be considered as an unstable configuration.
