Anomalous and Quantum Hall Effects in Lossy Photonic Lattices

TL;DR

This paper explores how anomalous and integer quantum Hall effects can be simulated in driven-dissipative photonic lattices with synthetic gauge fields, providing a potential method for experimental measurement of topological properties.

Contribution

It introduces a theoretical framework for observing quantum Hall effects in lossy photonic systems and links the transverse light shift to topological invariants like Chern number and Berry curvature.

Findings

Transverse shift proportional to Chern number or Berry curvature.

Potential for experimental measurement of topological invariants.

Demonstrates effects in driven-dissipative photonic lattices.

Abstract

We theoretically discuss analogues of the anomalous and the integer quantum Hall effect in driven-dissipative two-dimensional photonic lattices in the presence of a synthetic gauge field. Photons are coherently injected by a spatially localized pump, and the transverse shift of the in-plane light distribution under the effect of an additional uniform force is considered. Depending on pumping parameters, the transverse shift turns out to be proportional either to the global Chern number (integer quantum Hall effect) or to the local Berry curvature (anomalous Hall effect). This suggests a viable route to experimentally measure these quantities in photonic lattices.