Non-Hermitian Quantum Geometric Tensors in an Exciton-Polariton System

Yow-Ming (Robin) Hu, ANU

Topological electronic materials and photonic systems have attracted a great amount of interests because they exhibit robust edge states that could enable unidirectional, loss-less transport of charge carriers or photons. Topological phases in both electronic and photonic systems are typically signaled by non-zero values of certain topological invariants in the band structure [1].

Recently, the study of topological effects was generalized to open dissipative systems described by non-Hermitian Hamiltonians, which lead to a wide range of effects such as coherent-perfect absorption and lasing, directional emission, as well as novel topological invariants and edge states [2]. A hybrid light-matter system of microcavity exciton polaritons, which arise from the strong coupling of excitons in a semiconductor and cavity photon modes, represents an accessible platform for studies of non-Hermitian effects, including the novel topology.

Previous work has demonstrated that the exciton polaritons can be used to experimentally measure a quantity called the quantum geometric tensor [3,4]. The quantum geometric tensor is a complex-valued tensor. Its imaginary component corresponds to a topological effective magnetic field in momentum space known as the Berry curvature, and its real part is the quantum metric tensor that defines the distance between two quantum states [5].

Recently, this quantum geometric tensor has been generalized to non-Hermitian systems [6-8]. Due to the bi-orthogonal left and right eigenvectors of the non-Hermitian systems [2], there exist two different ways to define components of the generalized quantum geometric tensor. One is defined using only the right eigenvector (which we denote as RR) [6,7], while the other is defined using both the left and right eigenstates (which we denote as LR) [8]. However, only the RR Berry curvature [6] and quantum metric [7] have been experimentally measured so far.

In this work, we calculate the components of the two generalized quantum geometric tensors in an exciton-polariton system. We also extend the formalism presented in Ref. [3] and show that the LR generalizations of the quantum geometric tensor can be experimentally measured. Our results suggest further directions for exploring non-Hermitian topology using exciton polaritons.

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