Quantum optics measurement scheme for quantum geometry and topological invariants

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.

16 pages, 4 figures

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Cited by in corpus (9)

• Optical manifestations and bounds of topological Euler class
• Identifying non-Hermitian critical points with quantum metric
• Non-Abelian quantum geometric tensor in degenerate topological semimetals
• Quantum geometric bounds for observables: Linear responses, Drude weight, and orbital magnetization
• Cavity Spectroscopy for Strongly Correlated Systems
• Quantum geometric bounds in spinful systems with trivial band topology
• Quantum Metric-induced Oscillations in Flat Bands
• Spin-polarized scanning tunneling microscopy measurement scheme for determining the quantum geometric tensor
• Probing the collective excitations of excitonic insulators in an optical cavity