Two-dimensional waveguide quantum electrodynamics

Waveguide QED has emerged as a subfield of quantum optics, focusing on the study of quantum emitters coupled to various one-dimensional photonic structures, such as waveguides and photonic crystals. The strong coupling between emitters and photons, combined with the ability to confine light in lower dimensions, makes waveguide QED platforms ideal for exploring strong atom-photon and photon-photon interactions. These platforms also potentially enable the generation of complex quantum states of light and the development of quantum networks and waveguide QED based quantum simulators. Although waveguide QED initially concentrated on one-dimensional systems, there has been growing interest in studying quantum emitters coupled to two-dimensional photonic structures. In this doctoral thesis, we investigate two-dimensional arrays of atoms coupled to photonic structures. We first discuss the emergence of long-lived states that exhibit strong photon-photon interactions in these systems. Specifically, we demonstrate the existence of both repulsive and attractive states, with the latter manifesting as photon-photon bound states. After that, we engineer a system consisting of a two-dimensional array of quantum emitters coupled to a square network of one-dimensional waveguides that exhibit a flat band. This system also hosts compact localizes states, eigenstates of the system given by the superposition of the flat bands’ Bloch waves, in which the photons are localized on the finite number of unit cells. This result is particularly intriguing, as compact localized states typically appear in systems with finite-range interactions. We also demonstrate that in the presence of multiple excitations, interaction-induced transport emerges in the form of dispersive bound states. Finally, we examined how atomic motion influences the internal degrees of freedom of atoms coupled to a photonic structure. Motional effects are particularly intriguing for atoms trapped in close proximity to photonic structures, as they experience strong Casimir- Polder forces. The strength of the Casimir-Polder potential depends on the atom’s internal state and its distance from the nanophotonic structure, effectively inducing a positiondependent Lamb shift in the atoms. We demonstrate that, when the atoms are not tightly trapped and cannot be considered static, this Lamb shift can lead to decoherence of their internal degrees of freedom and contribute to unwanted atomic heating.