Topological growing of Laughlin states in synthetic gauge fields

TL;DR

This paper proposes a method to generate Laughlin states in synthetic gauge field systems by sequentially adding composite fermions and flux quanta, enabling controlled growth of highly correlated quantum states.

Contribution

It introduces a novel protocol for growing Laughlin states using topologically protected flux insertion and particle filling, applicable to photonic and atomic systems.

Findings

Numerical simulations confirm the feasibility of the protocol.

The method allows linear growth of particle number with suppressed fluctuations.

The scheme is robust against losses in 2D lattice systems.

Abstract

We suggest a scheme for the preparation of highly correlated Laughlin (LN) states in the presence of synthetic gauge fields, realizing an analogue of the fractional quantum Hall effect in photonic or atomic systems of interacting bosons. It is based on the idea of growing such states by adding weakly interacting composite fermions (CF) along with magnetic flux quanta one-by-one. The topologically protected Thouless pump ("Laughlin's argument") is used to create two localized flux quanta and the resulting hole excitation is subsequently filled by a single boson, which, together with one of the flux quanta forms a CF. Using our protocol, filling 1/2 LN states can be grown with particle number N increasing linearly in time and strongly suppressed number fluctuations. To demonstrate the feasibility of our scheme, we consider two-dimensional (2D) lattices subject to effective magnetic fields and strong on-site interactions. We present numerical simulations of small lattice systems and discuss also the influence of losses.