  We report the Bose-Einstein condensate (BEC) in the Bloch bands with
off-diagonal periodic potential (ODPP), which simultaneously plays the role of
spin-orbit coupling (SOC) and Zeeman field. This model can be realized using
two independent Raman couplings in the same three level system, in which the
time-reversal symmetry ensures the energy degeneracy between the two states
with opposite momenta. We find that these two Raman couplings can be used to
tune the spin polarization in momentum space, thus greatly modifies the
effective scatterings over the Bloch bands. We observe a transition from the
Bloch plane wave phase with condensate at one wave vector to the Bloch stripe
phase with condensates at the two Bloch states with opposite wave vectors.
These two phases will exhibit totally different spin textures and density
modulations in real space, which are totally different from that in free space.
In momentum space multiple peaks differ by some reciprocal lattice vectors can
be observed, reflecting the periodic structure of the ODPP. A three-band
effective model is proposed to understand these observations. This system can
provide a new platform in investigating of various physics, such as collective
excitations, polaron and topological superlfuids, over the Bloch bands.
