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Revealing the quantum geometry of Bloch electrons through light-matter coupling

Michael Schüler

University of Fribourg

The quantum geometry of Bloch electrons in solids plays a fundamental role for material properties, in particular for transport and light-matter interaction. Topological properties, Berry curvature, polarization, and orbital angular momentum are all examples of quantum-geometric properties. Directly measuring the quantum geometry is a grand challenge, while dynamically manipulating the properties of electrons would unlock ultrafast control of topological properties.
In the first part of the talk, we will discuss how Berry curvature of two-dimensional (2D) materials can be extracted using pump-probe time- and angle-resolved photoemission (trARPES). We show that the concept of momentum-resolved transitions rates, which originates from the field of ultracold atoms in optical lattices, can thus be transferred to materials. We demonstrate the general methodology both theoretically and experimentally for atomically thin WSe[1].
In the second part of the talk we will extend the ideas to interaction of quantized photons in a cavity with solids. The resulting light-matter hybrid state leaves a specific fingerprint in the photon-photon correlations that can be probed by quantum-optics setups. Exploiting the link between the quantum geometry and the strength of light-matter coupling, we will establish bounds on the photon correlations that allow for distinguishing different topological phases, and allow us in principle to extract topological invariants such as the Euler number in twisted bilayer graphene [2].

[1] Beaulieu, S., Berry Curvature Signatures in Chiroptical Excitonic Transitions. Preprint at (2023)
[2] Lysne, M., Schüler, M. & Werner, P. Quantum Optics Measurement Scheme for Quantum Geometry and Topological Invariants. Phys. Rev. Lett. 131, 156901 (2023).