  Raman-assisted hopping can allow for the creation of density-dependent
synthetic magnetism for cold neutral gases in optical lattices. We show that
the density-dependent fields lead to a non-trivial interplay between density
modulations and chirality. This interplay results in a rich physics for atoms
in two-leg ladders, characterized by a density-driven Meissner- to
vortex-superfluid transition, and a non-trivial dependence of the density
imbalance between the legs. Density-dependent fields also lead to intriguing
physics in square lattices. In particular, it leads to a density-driven
transition between a non-chiral and a chiral superfluid, both characterized by
non-trivial charge density-wave amplitude. We finally show how the physics due
to the density-dependent fields may be easily probed in experiments by
monitoring the expansion of doublons and holes in a Mott insulator, which
presents a remarkable dependence on quantum fluctuations.
