  The realization and detection of topological phases with ultracold atomic
gases is at the frontier of current theoretical and experimental research.
Here, we identify cold atoms in optical ladders subjected to synthetic magnetic
fields as readily realizable bridges between one-dimensional spin-orbit (time
reversal) topological insulators and two-dimensional Chern insulators. We
reveal three instances of their promising potential: i) they realize spin-orbit
coupling, with the left-right leg degree of freedom playing the role of an
effective spin, ii) their energy bands and eigenstates exactly reproduce the
topological chiral edge modes of two-dimensional Chern insulators, and iii)
they can be tailored to realize a topological phase transition from a trivial
to a topological insulating phase. We propose realistic schemes to observe the
chiral and topological properties of ladder systems with current optical
lattice-based experiments. Our findings open a door to the exploration of the
physics of the edges of Chern insulators and to the realization of spin-orbit
coupling and topological superfluid phases with ultracold atomic gases.
