Spectroscopy and topological properties of a Haldane light system

We present a method to probe the topological properties of a circuit quantum electrodynamics (cQED) array described through a Haldane model on the honeycomb lattice. We develop the theory of microwave light propagating in a local probe or a microscope (a one-dimensional transmission line) capacitively coupled to the topological cQED lattice model. Interestingly, we show that even if the microwave light has no transverse polarization, the measured reflection coefficient, resolved in frequency through the resonance, allows us to reveal the geometrical properties and topological phase transition associated to the model. This spectroscopy tool developed for cQED lattice models reveals the same topological information as circularly polarized light, locally within the Brillouin zone of the honeycomb lattice. Furthermore, our findings hold significance for topological magnon systems and are a priori applicable to all Chern insulators, presenting an intriguing opportunity for their adaptation to other systems with different particle statistics.