Topological and Localised States in Waveguide Quantum Electrodynamics

Abstract

Waveguide quantum electrodynamics (QED) is a subfield of quantum optics that studies arrays of atoms coupled to a waveguide. Confining the propagation of light to a one-dimensional (1D) channel enhances the atom-photon interaction strength which is crucial for many quantum information applications. It also allows for infinite-range atom-atom interactions mediated by photons which gives rise to a plethora of exotic effects such as the fermionisation of photons, interaction-induced localisation, bound photons and even quantum chaos. The first part of this thesis is about the numerical results in Ref. [1]. I focus on a specific kind of localisation in the two-photon subspace of waveguide QED which are self-induced topological edge states. The hallmarks of the quantum Hall effect can be found in our model, from Landau levels to a Hofstadter-like butterfly energy spectrum. The second part of this thesis focuses on Ref. [2]. I provide the first classification of eigenstates in the three-photon subspace of waveguide QED and show that the rich interplay of order, chaos and localisation found in two-photon systems extends naturally to three-photon systems. There also exist interaction-induced localised states unique to three-photon systems such as bound trimers, corner states and trimer edge states. Our results show that there are many exotic and unexplored effects within interacting waveguide QED systems.

[1] Poshakinskiy, Alexander V., et al. "Quantum Hall phases emerging from atom-photon interactions." npj Quantum Information 7.1 (2021): 1-8. [2] Zhong, Janet, and Alexander N. Poddubny. "Classification of three-photon states in waveguide quantum electrodynamics." Physical Review A 103.2 (2021): 023720.