  We study bosonic and fermionic quantum two-leg ladders with orbital magnetic
flux. In such systems, the ratio, $\nu$, of particle density to magnetic flux
shapes the phase-space, as in quantum Hall effects. In fermionic (bosonic)
ladders, when $\nu$ equals one over an odd (even) integer, Laughlin fractional
quantum Hall (FQH) states are stabilized for sufficiently long ranged repulsive
interactions. As a signature of these fractional states, we find a unique
dependence of the chiral currents on particle density and on magnetic flux.
This dependence is characterized by the fractional filling factor $\nu$, and
forms a stringent test for the realization of FQH states in ladders, using
either numerical simulations or future ultracold-atom experiments. The two-leg
model is equivalent to a single spinful chain with spin-orbit interactions and
a Zeeman magnetic field, and results can thus be directly borrowed from one
model to the other.
