  We present a quantum Monte Carlo study of the one-body density matrix (OBDM)
and the momentum distribution of one-dimensional dipolar bosons, with dipole
moments polarized perpendicular to the direction of confinement. We observe
that the long-range nature of the dipole interaction has dramatic effects on
the off-diagonal correlations: although the dipoles never crystallize, the
system goes from a quasi-condensate regime at low interactions to a regime in
which quasi-condensation is discarded, in favor of quasi-solidity. For all
strengths of the dipolar interaction, the OBDM shows an oscillatory behavior
coexisting with an overall algebraic decay; and the momentum distribution shows
sharp kinks at the wavevectors of the oscillations, $Q = \pm 2\pi n$ (where $n$
is the atom density), beyond which it is strongly suppressed. This
\emph{momentum filtering} effect introduces a characteristic scale in the
momentum distribution, which can be arbitrarily squeezed by lowering the atom
density. This shows that one-dimensional dipolar Bose gases, realized e.g. by
trapped dipolar molecules, show strong signatures of the dipolar interaction in
time-of-flight measurements.
