Topological Protection and Emission Control in a Waveguide Quantum Electrodynamical SystemTools McDonnell, Ciarán (2023) Topological Protection and Emission Control in a Waveguide Quantum Electrodynamical System. PhD thesis, University of Nottingham.
AbstractIn this thesis we explore methods for controlling and protecting quantum processes in a QED system. We begin with an explanation of how topology can arise in physics before deriving the quantum optical master equation of identical two-level atoms coupled to a one-dimensional nanofiber waveguide. We analyze the topological and dynamical properties of a system formed by placing the atoms in two chains, whose interactions with the guided modes of the nanofiber induce all-to-all excitation hopping. We find that, in the single excitation limit, the bulk topological properties of the Hamiltonian that describes the coherent dynamics of the system are identical to the ones of a one-dimensional Su-Schrieffer-Heeger (SSH) model. We confirm this in the short-range interacting limit by showing the bulk-boundary correspondence - the emergence of robust edge states in the topologically non-trivial phase of the model. Upon extending the range of interactions however, we find weakening of this bulk-boundary correspondence. This is illustrated by the variation of the localization length and mass gap of the edge states encountered as we vary the lattice constant and offset between the chains. Most interestingly, we analytically identify parameter regimes where edge states arise which are fully localized to the boundaries of the chain, independently of the system size. These edge states are shown to be not only robust against positional disorder of the atoms in the chain, but also subradiant, i.e., dynamically stable even in the presence of inevitable dissipation processes. Furthermore we show how the population of an edge excitation can be transported from one end of the chain to the other and how one can engineer different dynamical properties of the edge excitations, such as superradiant decay.
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