Gain induced topological response via tailored long range interactions
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 settings1,2. 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 correspondence3 8. 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 behaviours induced by optical gain. As a demonstration, we implement the Haldane model, a canonical lattice that relies on asymmetric long range hopping to exhibit quantum Hall behaviour 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 open up avenues to study the role of gain and nonlinearity in topological systems in the presence of quantum noise. Non Hermitian concepts together with optical gain allow the tailoring of short and long range exchange interactions in integrated topological photonics, and an exact Haldane model can be realized in this way.