Gain Induced Topological Response via Tailored Long-range Interactions

TL;DR

This paper demonstrates how tailored asymmetric long-range interactions in photonic systems, induced by optical gain, can realize topological phenomena like the quantum Hall effect without magnetic flux, opening new research avenues.

Contribution

It introduces a method to implement asymmetric long-range hopping in photonic platforms using non-Hermitian gain, enabling topological effects without magnetic fields.

Findings

Realized the Haldane model with gain-induced topological response.

Observed topological behavior that vanishes in passive structures.

Showed potential for studying gain and nonlinearity effects in topological systems.

Abstract

The ability to tailor the hopping interactions between the constituent elements of a physical system could enable the observation of unusual phenomena that are otherwise inaccessible in standard settings. In this regard, a number of recent theoretical studies have indicated that an asymmetry in either the short- or long-range complex exchange constants can lead to counterintuitive effects, for example, the possibility of a Kramer's degeneracy even in the absence of spin 1/2 or the breakdown of the bulk-boundary correspondence. Here, we show how such tailored asymmetric interactions can be realized in photonic integrated platforms by exploiting non-Hermitian concepts, enabling a class of topological behaviors induced by optical gain. As a demonstration, we implement the Haldane model, a canonical lattice that relies on asymmetric long-range hopping in order to exhibit quantum Hall behavior without a net external magnetic flux. The topological response observed in this lattice is a result of gain and vanishes in a passive but otherwise identical structure. Our findings not only enable the realization of a wide class of non-trivial phenomena associated with tailored interactions, but also opens up avenues to study the role of gain and nonlinearity in topological systems in the presence of quantum noise.