  We report an experimental demonstration of engineering phase wraps for
sub-wavelength structure in a Bose-Einstein condensate (BEC) with
two-dimensional optical lattices. A short lattice pulse is applied on BEC
working in the Kapitza-Dirac (or Raman-Nath) regime, which corresponds to phase
modulation imprint on matter wave. When the phase modulation on matter wave is
larger than $2\pi$ in a lattice cell, there appears phase wraps with multiple
$2\pi$ jumps, generating the sub-wavelength phase structure. The phase wraps
for sub-wavelength structure are measured in momentum space via the
time-of-flight absorption image, which corresponds to converting phase
information into amplitude. %Two different kinds of two-dimensional optical
lattice are studied, which show the different subwavelength phase structure.
Moreover, we identify an additional condition for the validity of Kapitza-Dirac
regime, which relies crucially on the lattice configurations. This scheme can
be used for studying the property of optical lattices and topological defects
in matter wave.
