Entangled multi-component 4D quantum Hall states from photonic crystal defects

TL;DR

This paper proposes a realistic method to realize multi-component topological phases, including an entangled 4D quantum Hall state, in 2D photonic crystals with defect modulations, enabling novel topological photonic applications.

Contribution

It introduces a versatile approach to create multi-component topological states in photonic crystals using defect modulations, including the first realization of an entangled 4D QH phase.

Findings

Realization of an entangled 4D quantum Hall phase in photonic crystals.

Demonstration of 4D p-orbital nodal lines with exotic boundary states.

Quantification of non-factorizability using classical entanglement entropy.

Abstract

Recently, there has been a drive towards the realization of topological phases beyond conventional electronic materials, including phases defined in more than three dimensions. We propose a versatile and experimentally realistic approach of realizing a large variety of multi-component topological phases in 2D photonic crystals with quasi-periodically modulated defects. With a length scale introduced by a background resonator lattice, the defects are found to host various effective orbitals of $s$, $p$ and $d$-type symmetries, thus providing a monolithic platform for realizing multi-component topological states without requiring separate internal degrees of freedom in the physical setup. Notably, by coupling the defect modulations diagonally, we report the novel realization of an ``entangled'' 4D QH phase which cannot be factorized into two copies of 2D QH phases, each described by the 1st Chern number. The structure of this non-factorizability can be quantified by a classical entanglement entropy inspired by quantum information theory. In another embodiment, we present 4D p-orbital nodal lines in a nonsymmorphic photonic lattice, hosting boundary states with an exotic manifold. Our simple and versatile approach holds the promise of novel topological optoelectronic and photonic applications such as one-way optical fibers.