Laughlin-like states in bosonic and fermionic atomic synthetic ladders

TL;DR

This paper demonstrates how synthetic atomic ladders can host Laughlin-like states, revealing a pathway to explore complex two-dimensional quantum phenomena such as fractional quantum Hall effects in controlled one-dimensional systems.

Contribution

It provides theoretical evidence and diagnostic tools for identifying Laughlin-like states in synthetic ladders, highlighting their distinct signatures and phase transitions.

Findings

Laughlin-like states can be observed in synthetic ladders

Distinct signatures include chiral current and entanglement entropy

Transitions characterized by sharp current discontinuities

Abstract

The combination of interactions and static gauge fields plays a pivotal role in our understanding of strongly-correlated quantum matter. Cold atomic gases endowed with a synthetic dimension are emerging as an ideal platform to experimentally address this interplay in quasi-one-dimensional systems. A fundamental question is whether these setups can give access to pristine two-dimensional phenomena, such as the fractional quantum Hall effect, and how. We show that unambiguous signatures of bosonic and fermionic Laughlin-like states can be observed and characterized in synthetic ladders. We theoretically diagnose these Laughlin-like states 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. Remarkably, Laughlin-like states are separated from conventional liquids by Lifschitz-type transitions, characterized by sharp discontinuities in the current profiles, which we address using extensive simulations based on matrix-product states. Our work provides a qualitative and quantitative guideline towards the observability and understanding of strongly-correlated states of matter in synthetic ladders. In particular, we unveil how state-of-the-art experimental settings constitute an ideal starting point to progressively tackle two-dimensional strongly interacting systems from a ladder viewpoint, opening a new perspective for the observation of non-Abelian states of matter.