Generalized Quantum Geometric Tensor in a Non-Hermitian Exciton-Polariton System

Abstract

In this work, we review different generalizations of the quantum geometric tensor (QGT) in two-band non-Hermitian systems and propose a protocol for measuring them in experiments. We present the generalized QGT components, i.e. the quantum metric and Berry curvature, for a non-Hermitian hybrid photonic (exciton-polariton) system and show that the generalized non-Hermitian QGT can be constructed from experimental observables. In particular, we extend the existing method of measuring the QGT that uses the pseudospins in photonic and exciton-polariton systems by suggesting a method to construct the left eigenstates from experiments. We also show that the QGT components have clear signatures in wave-packet dynamics, where the anomalous Hall drift arises from both the non-Hermitian Berry curvature and Berry connection, suggesting that both left and right eigenstates are necessary for defining non-Hermitian band geometries and topologies.

30 pages, 11 figures

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• Characterizing phase transitions and criticality in non-Hermitian extensions of the XY model
• Adiabatic Transformations in Dissipative and Non-Hermitian Phase Transitions
• Topological invariants and topological charges in photonic systems
• Direct measurement of the quantum geometric tensor in pseudo-Hermitian systems
• Breakdown of Bulk-Radiation Correspondence in Radiative Photonic Lattices
• Topological photonics in nanoscaled systems with far field radiation and polarization singularities
• Minimal Hamiltonian deformations as bulk probes of effective non-Hermiticity in Dirac materials
• Multi-block exceptional points in open quantum systems
• Non-Hermitian wave-packet dynamics and its realization within a non-Hermitian chiral cavity
• Exceptional flat bands in bipartite non-Hermitian lattices
• Fidelity and quantum geometry approach to Dirac exceptional points in diamond nitrogen-vacancy centers