Spectroscopy and topological properties of a Haldane light system

TL;DR

This paper introduces a real-space spectroscopic method to probe topological properties in a 2D cQED array, demonstrating how microwave reflection measurements reveal topological phases and transitions.

Contribution

It develops a novel local spectroscopic technique for 2D topological photonic systems and links measurable reflection coefficients to topological invariants.

Findings

Reflection coefficient reveals topological phase transition

Method applicable to 2D cQED arrays

Physical parameters affect measurement stability

Abstract

We introduce a local spectroscopic method in real space to probe the topological properties of a circuit quantum electrodynamics (cQED) array generalizing previous approaches from one to two dimensions in the plane. As an application, we develop the theory of microwave light propagating in the local probe capacitively coupled to the cQED array associated to a bosonic Haldane model. Interestingly, we show that the measured reflection coefficient, resolved in frequency through the resonance, reveals the geometrical properties of the model and the topological phase transition. We discuss the role of physical parameters such as the lifetime of the light modes and stability towards local disorder related to further realizations.