Non-Hermitian effects in exciton-polariton systems

In this thesis we study non-Hermitian aspects of exciton-polariton Bose-Einstein condensates. Exciton-polaritons are hybrid matter-light quasiparticles created when microcavity photons are strongly coupled to quantum well excitons, which are bound electron-hole pairs. Being composite bosons with a very low effective mass, exciton-polaritons can undergo Bose-Einstein condensation at relatively high temperatures - from cryogenic to as high as room temperature in some semiconductors. Exciton-polariton condensates are an experimentally attractive system due to the high transition temperature and ease of in-situ diagnostics. They are also fundamentally non-Hermitian because they exist in a balanced landscape of loss and gain, where excitation by a pump laser counteracts the radiative decay of polaritons. Because of their hybrid light-matter nature exciton-polariton condensates are also an ideal platform for designing new optoelectronic devices, and non-Hermitian effects may be useful to this end. Hermiticity is posited as an axiom of quantum mechanics in order to ensure that energies are real. However in recent decades it has been shown that a class of non-Hermitian Hamiltonians which adhere to a weaker condition of symmetry under simultaneous spatial and time reversal (PT symmetry) can still have real energies. Many of the essential features of Hermitian quantum mechanics can be reproduced with such Hamiltonians. In general PT symmetric systems exhibit two phases, one in which eigenvalues are real, and another in which the eigenvectors spontaneously break the PT symmetry and eigenvalues are complex. The transition occurs at an exceptional point, a non-Hermitian degeneracy where eigenstates coincide as well as eigenvalues. EPs can also be observed in non-Hermitian systems lacking PT symmetry. This has led to a collection of interesting experiments in optical and other systems that provide analogues of non-Hermitian quantum mechanics because loss and gain are represented by an imaginary potential. In these systems PT symmetry breaking has allowed for enhanced sensing, loss-induced transparency, gain-induced suppression of lasing, and sensitive switching. Exciton-polaritons condensates are inherently non-Hermitian as they experience loss and gain. However this aspect has been largely overlooked, apart from a few experiments which demonstrate EPs. Experiments in optical and other systems suggest that non-Hermitian effects in polaritons may be harnessed to design optoelectronic devices. In addition, the demonstration of PT symmetry breaking in yet another system is of inherent intellectual interest. We aim to provide theoretical guidance for current and future experiments that exploit the non-Hermiticity of polariton condensates. One chapter focuses on a very simple PT symmetric system - a PT symmetric square well for polaritons. Ths system is simple enough to be analytically tractable, but also exhibits interesting and subtle behaviour. We show how a nearly-PT symmetric square well can be implemented for polaritons using established trapping techniques. We further show that unavoidable PT asymmetry removes the PT symmetry breaking transition, but that most of this behaviour can easily be restored. In support of recent experiments, another part of the work focuses on whispering gallery modes (WGMs) of polariton condensates in a shallow circular trap. We show that an interesting experimental effect - a robust blueshift of half a free spectral range under certain pumping conditions - can be attributed to coupling with a non-Hermitian resonator. We also discuss the viability of various schemes for reaching EPs of polariton WGMs, and present preliminary numerical results which show that some of these schemes are viable. The research presented in this thesis provides a road map for future experimental and theoretical work that will harness non-Hermitian effects beyond the observation of EPs in polariton condensates