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The combination of interactions and static gauge fields plays a pivotal rolein our understanding of strongly-correlated quantum matter. Cold atomic gasesendowed with a synthetic dimension are emerging as an ideal platform toexperimentally address this interplay in quasi-one-dimensional systems. Afundamental question is whether these setups can give access to pristinetwo-dimensional phenomena, such as the fractional quantum Hall effect, and how.We show that unambiguous signatures of bosonic and fermionic Laughlin-likestates can be observed and characterized in synthetic ladders. We theoreticallydiagnose these Laughlin-like states focusing on the chiral current flowing inthe ladder, on the central charge of the low-energy theory, and on theproperties of the entanglement entropy. Remarkably, Laughlin-like states areseparated from conventional liquids by Lifschitz-type transitions,characterized by sharp discontinuities in the current profiles, which weaddress using extensive simulations based on matrix-product states. Our workprovides a qualitative and quantitative guideline towards the observability andunderstanding of strongly-correlated states of matter in synthetic ladders. Inparticular, we unveil how state-of-the-art experimental settings constitute anideal starting point to progressively tackle two-dimensional stronglyinteracting systems from a ladder viewpoint, opening a new perspective for theobservation of non-Abelian states of matter.

Laughlin-like states in bosonic and fermionic atomic synthetic ladders