Quantum optics measurement scheme for quantum geometry and topological invariants

TL;DR

This paper proposes a quantum optical measurement scheme using heterodyne detection to probe the geometrical and topological properties of 2D materials, enabling the extraction of quantum geometric tensors and topological invariants.

Contribution

It introduces a novel heterodyne detection-based method to measure quantum geometric and topological invariants in condensed matter systems via cavity photon correlations.

Findings

Correlation functions relate to the hybrid light-matter state.

All components of the quantum geometric tensor can be accessed.

Topological phases and spin Chern numbers can be characterized.

Abstract

We show how a quantum optical measurement scheme based on heterodyne detection can be used to explore geometrical and topological properties of condensed matter systems. Considering a 2D material placed in a cavity with a coupling to the environment, we compute correlation functions of the photons exiting the cavity and relate them to the hybrid light-matter state within the cavity. Different polarizations of the intracavity field give access to all components of the quantum geometric tensor on contours in the Brillouin zone defined by the transition energy. Combining recent results based on the metric-curvature correspondence with the measured quantum metric allows us to characterize the topological phase of the material. Moreover, in systems where $S_z$ is a good quantum number, the procedure also allows us to extract the spin Chern number. As an interesting application, we consider a minimal model for twisted bilayer graphene at the magic angle, and discuss the feasibility of extracting the Euler number.