Non-Hermitian Topology of Microcavity Exciton Polaritons

Abstract

Topology in solid state physics gave a new way to classify materials using quantities called topological invariants. Phases with non-vanishing topological invariants can exhibit non-trivial dynamics of charge-carriers at the boundary which is protected against scattering with impurities and imperfections. The study of topology has recently been generalized to a new class of systems with dissipation, which can be described by effective non-Hermitian Hamiltonians and have complex-valued eigenenergies. It has been discovered that there are topological invariants unique to non-Hermitian systems. One of them—spectral winding arises near the exceptional points (the non-Hermitian spectral degeneracies). In this thesis, I investigated the non-Hermitian topology of a mixed light-matter system—microcavity exciton polaritons. The exciton polaritons are composite particles created by strongly coupling bound electron-hole pairs (excitons) to photons in a microcavity. They can be described by a non-Hermitian Hamiltonian because both gain (via optical pumping) and loss (radiative decay) are always present in the system. The ANU Polariton BEC group has previously observed a non-Hermitian spectral degeneracy in this system and, in a separate study, detected the spectral winding around a pair of the exceptional points. However, a comprehensive theory of non-Hermitian topology for this system has not yet been developed. In this thesis, I took the first essential steps towards building a theoretical framework for studies of non-Hermitian topology in exciton-polariton systems. In particular, I derived quantities that characterise the global properties of the eigenvalues that are analogous to those used in Hermitian topological systems. One important topological invariant in the solid state system is the Chern number. The Chern number is realted to a quantity called the Berry curvature, which acts on the electrons in the solid state system as an effective magnetic field when an external field is absent. The Berry curvature is part of a larger quantity called the quantum geometric tensor. The real part of quantum geometric tensor is a metric that defines the distance between two states in momentum space, while its imaginary part is related to the Berry curvature. In this thesis, I generalized the quantum geometric tensor to non- Hermitian systems using a recently developed formalism (Chapter 4). I then investigated the properties of the components of the four quantum geometric tensors and concluded that two of them are the natural non-Hermitian generalizations, while the remaining ones are inconsistent (Chapter 5). This conclusion was further supported by investigation of exciton-polariton wavepacket dynamics (Chapter 6). The last Chapter of this thesis summarises conclusions drawn from my study and presents an outlook on further research.