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In this thesis, we study topological phases and phenomena in quantum many-body atomic systems coupled to a common environment. Atoms coupled to a common environment display collective behaviour, including induced long-range dipole-dipole interactions and collective dissipation of excitations into the environment. Many-body quantum optical systems are promising platforms to study topological phases due to the high degree of control of the system parameters that can be achieved by changing, for example, the interatomic spacings. Coupling the atomic system to a structured environment, like a dielectric or metallic structure, allows for tailoring the dipole-dipole interactions to reach a given strength and range of interactions. Interactions can even be made all-to-all by coupling the atoms to a nanophotonic waveguide. The high control of the interactions enables both the study of existing topological models and the exploration of new ones with long-range interactions, where little is known about the fate of topological properties. Furthermore, the controllable interactions enable the study of topological transport mechanisms such as topological pumping, which is based on cyclic variation of the Hamiltonian parameters. As a result of the collective behaviour, topological phases can be made subradiant, which allows for the study of long-lived topological dynamics.
In the first original work resulting from the work in this Thesis, we derive the induced dipole-dipole interactions between an ensemble of atoms coupled to a nanophotonic waveguide by means of the electromagnetic Green's tensor. We derive, analytically, the all-to-all dipole-dipole interactions stemming from the guided modes of the waveguide. Moreover, we provide, for the first time, a numerical method for computing with high precision, the unguided contribution to the dipole-dipole interactions. This interaction differs significantly from its free space counterpart, especially when the atoms are close to the waveguide surface. We illustrate this by comparing the transmission of fiber-guided light from free space modes and the numerically computed unguided modes, where not only the resonance peaks are shifted, but an overall deformation of the transmission spectrum is evident for a large atomic system size.
In the second and third original works, we study the existence of topological phases in many-body quantum optical systems in the presence of long-range to all-to-all interactions. In particular, we study the robust topological transport of a photon embedded in a one-dimensional chain in three relevant quantum optics platform, namely Rydberg atoms, atoms in low-lying states in free space and atoms coupled to a nanophotonic waveguide. We show topological transport of a photon, which is robust against local disorder in the atomic position. The transport can be performed subradiantly in the case of atoms in low-lying states and atoms coupled to a waveguide, or within the lifetime of the Rydberg atoms. Finally, we present a two-dimensional topological model with Rydberg atoms. The model displays a myriad of distinct topological phases, including two weak topological insulating phases, characterized by edge states occupying only one boundary, and a weakly broken higher order topological insulating phase with corner-like states. Moreover, a semi-metallic phase is found manifested by a pair of oppositely topologically charged and tunable Dirac points and associated tilted and anisotropic cones. For specific parameter choices, the Dirac points collapse into nodal lines. |
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