Topological Protection and Emission Control in a Waveguide Quantum Electrodynamical System - McDonnell, Ciarán (2023)
In 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. We next examine the guided emission properties of the atoms coupled to the nanofiber waveguide via weak laser-driving. We first investigate the effects of varying the spacing between atoms in the same and different chains and find that the fiber coupling efficiency, as well as the flux of the guided emission are maximised when neighbouring atoms are separated by a multiple of the wavelength of the light in the nanofiber, satisfying the modified Bragg condition. These two observables increase with the system size before saturating for large enough atom numbers. Moreover, we find that placing the two chains on opposite sides of the nanofiber allows us to enhance both the FCE and the guided photon flux even further. Moreover, these observables are optimized further by choosing an appropriate value of the detuning between the laser and atomic frequency. Next we study the correlation properties of the photon emission into the guided modes. For a system of two atoms driven by a resonant laser on the same side or opposite sides of the fiber, we find that by varying the distance between the atoms the same-time photon correlation functions can exhibit photon bunching or anti-bunching. Furthermore, the time-separated correlation functions of photons emitted by atoms above the nanofiber may exhibit persistent quantum beat behaviour for fixed atomic separation between the atoms. No such beats are found when the atoms are on opposite sides of the fiber. The overall size of the photon bunching and anti-bunching effects exhibited by same-time correlations are found to reduce with increased system size, suggesting that large system sizes may only exhibit coherent photon emission.