  We propose a technique for engineering momentum-dependent dissipation in
Bose-Einstein condensates with non-local interactions. The scheme relies on the
use of momentum-dependent dark-states in close analogy to velocity-selective
coherent population trapping. During the short-time dissipative dynamics, the
system is driven into a particular finite-momentum phonon mode, which in real
space corresponds to an ordered structure with non-local density-density
correlations. Dissipation-induced ordering can be observed and studied in
present-day experiments using cold atoms with dipole-dipole or off-resonant
Rydberg interactions. Due to its dissipative nature, the ordering does not
require artificial breaking of translational symmetry by an opticallattice or
harmonic trap. This opens up a perspective of direct cooling of quantum gases
into strongly-interacting phases.
