Direct measurement of the quantum geometric tensor in a two-dimensional continuous medium

Abstract

Topological Physics relies on the specific structure of the eigenstates of Hamiltonians. Their geometry is encoded in the quantum geometric tensor containing both the celebrated Berry curvature, crucial for topological matter, and the quantum metric. The latter is at the heart of a growing number of physical phenomena such as superfluidity in flat bands, orbital magnetic susceptibility, exciton Lamb shift, and non-adiabatic corrections to the anomalous Hall effect. Here, we report the first direct measurement of both Berry curvature and quantum metric in a two-dimensional continuous medium. The studied platform is a planar microcavity of extremely high finesse, in the strong coupling regime. It hosts mixed exciton-photon modes (exciton-polaritons) subject to photonic spin-orbit-coupling which makes emerge Dirac cones and exciton Zeeman splitting breaking time-reversal symmetry. The monopolar and half-skyrmion pseudospin textures are measured by polarisation-resolved photoluminescence. The associated quantum geometry of the bands is straightforwardly extracted from these measurements. Our results unveil the intrinsic chirality of photonic modes which is at the basis of topological photonics. This technique can be extended to measure Bloch band geometries in artificial lattices. The use of exciton-polaritons (interacting photons) opens wide perspectives for future studies of quantum fluid physics in topological systems.

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• Topological Insulators
• Anomalous Hall effect
• Topological Photonics
• Topological Photonics
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• Topological Acoustics
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• Exciton-polariton topological insulator
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• Topological Origin of Equatorial Waves
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• Slow reflection and two-photon generation of microcavity exciton-polaritons
• Effective Theory of Non-Adiabatic Quantum Evolution Based on the Quantum Geometric Tensor
• Measuring the Quantum Geometric Tensor in 2D Photonic and Polaritonic Systems
• Macroscopic Two-Dimensional Polariton Condensates
• Geometry of Bloch states probed by Stückelberg interferometry
• ${\mathbb{Z}}_2$ topological insulator analog for vortices in an interacting bosonic quantum fluid
• Wave packet dynamics of Bogoliubov quasiparticles: quantum metric effects
• Exceptional points in anisotropic planar microcavities

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• From Classical to Quantum Information Geometry: A Guide for Physicists
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• Quantum phase transitions in a spin-1 antiferromagnetic chain with long-range interactions and modulated single-ion anisotropy
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• Local geometry and quantum geometric tensor of mixed states
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