Adiabatic flux insertion and growing of Laughlin states of cavity Rydberg polaritons

TL;DR

This paper proposes a method to adiabatically insert flux quanta into cavity photons using external light fields and atomic mediators, enabling the preparation of fractional quantum Hall states like the Laughlin state in a cavity Rydberg polariton system.

Contribution

It introduces a novel flux insertion protocol combined with a growing scheme to create Laughlin states of cavity Rydberg polaritons, advancing quantum simulation of topological states.

Findings

Demonstrates flux insertion of 3ħ per step in cavity photons.

Proposes a protocol for growing Laughlin states via flux insertion and photon refilling.

Shows potential for realizing fractional quantum Hall states in photonic systems.

Abstract

Recently, the creation of photonic Landau levels in a twisted cavity has been demonstrated in Nature \textbf{534}, 671 (2016). Here we propose a scheme to adiabatically transfer flux quanta in multiples of $3\hbar$ simultaneously to all cavity photons by coupling the photons through flux-threaded cones present in such cavity setup. The flux transfer is achieved using external light fields with orbital angular momentum and a near-resonant dense atomic medium as mediator. Furthermore, coupling the cavity fields to a Rydberg state in a configuration supporting electromagnetically induced transparency, fractional quantum Hall states can be prepared. To this end a growing protocol is used consisting of a sequence of flux insertion and subsequent single-photon insertion steps. We discuss specifically the growing of the $\nu=1/2$ bosonic Laughlin state, where we first repeat the flux insertion twice creating a double quasi-hole excitation. Then, the hole is refilled using a coherent pump and the Rydberg blockade.