Dynamics, Topology and Quantum Geometry in non-Hermitian Exciton-Polariton Systems

Abstract

Open dissipative systems effectively described by non-Hermitian Hamiltonians have recently attracted a great amount of interests as they exhibit novel dynamics, topological invariants and topological edge states, to name a few. Non-Hermitian effects has been studied in a wide range of physical platforms, including mechanical, electronic, photonic, and condensed matter systems. However, the majority of this research is focused on periodic and discrete models. The effect of non-Hermiticity on truly continuous systems, especially those not subject to periodic potentials, is still an open problem. This PhD Thesis presents my research aimed at theoretically investigating this problem using an experimentally accessible condensed matter platform - microcavity exciton polaritons. These are two-dimensional (2D) quasiparticles arising from the strong coupling of electron-hole pairs (excitons) in direct-gap semiconductors and cavity photons. Exciton-polariton systems are inherently open-dissipative and allows for direct spectroscopic measurement of both real (energy) and imaginary (linewidth) part of their eigenenergy spectrum, as well as direct imaging of their eigenstates, making them an attractive platform for studies of non-Hermitian physics. First, I describe how an exciton-polariton wavepacket accelerates on its own in the absence of external fields. The self-acceleration arises from the inhomogeneous landscape in momentum space of the imaginary part of the eigenenergy. Using the same model, I then discuss the generalisation of the quantum geometric tensor to non-Hermitian systems, and explicitly show how their components, namely, the Berry curvature and the quantum metric tensor, can be measured experimentally and affect the wavepacket dynamics in the context of non-Hermitian perturbation theory. I also describe a non-Hermitian generalisation of the zitterbewegung effect of the exciton-polariton wavepacket, which exhibits sensitivity to the initial condition arising from the effective nonlinear pseudospin dynamics due to the non-Hermiticity. I also predict the emergence of topological defects in the pseudospin textures that exhibit different dynamics for two topologically distinct phases signaled by the presence and the absence of a non-Hermitian spectral degeneracy (an exceptional point). Finally, I investigate non-Hermitian topological edge states in momentum space and their potential realisation in an exciton-polariton system. The results presented in this Thesis show a wide range of new physics in non-Hermitian systems including novel dynamical effects, localisation of eigenstates ("edge effects"), generalised quantum geometric tensor and its role in the dynamics, as well as a new way of generating topological point defects. Importantly, these effects are not limited to exciton-polariton systems and can also be realised in other platforms, such as in photonic cavities and ultracold atomic gases with engineered loss.