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. of particle density to magnetic flux shapes the phase space, as in quantum Hall effects. In fermionic (bosonic) ladders, when. 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., 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.