Chiral currents in one-dimensional fractional quantum Hall states

We study bosonic and fermionic quantum two-leg ladders with orbital magnetic flux. In such systems, the ratio ν of particle density to magnetic flux shapes the phase space, as in quantum Hall effects. In fermionic (bosonic) ladders, when ν 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 ν, 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.