Laughlin-like states in bosonic and fermionic synthetic ladders

Laughlin-like states appear in ladder models which describe one-dimensional ultra-cold gases with a synthetic dimension: we show it explicitly both bosons and for fermions by studying several interacting microscopic models. For the bosonic case, we present explicit numerical results obtained with matrix-product states in the limit of weak tunneling in the synthetic direction. The fermionic case is instead addressed with an exactly-solvable model which describes Rydberg-dressed gases. We present extensive evidence that Laughlin-like physics can be diagnosed by focusing on the chiral current flowing in the ladder, on the central charge of the low-energy theory and on the properties of the entanglement entropy. The behavior of these observables is characterized with several analytical tools based on non-interacting models and bosonization; our predictions coincide with the numerical observations. Our work opens a novel route to the quantum simulation of the fractional quantum Hall effect with synthetic dimensions.