Abstract:
The subject of this thesis is the theoretical investigation of an atomic chain of Rydberg atoms
embedded in a photonic crystal waveguide. Atoms coupled to the photonic crystal show
prodigious coherent and dissipative dynamics. In coherent regime, the atoms interact via
the evanescent elds resulting in correlated many-body dynamics which demands powerful
numerical tool for modelling. The rst part of the thesis deals with the excitation dynamics
of Rydberg atoms in optical lattice. The excitation dynamics of a Rydberg atomic chain
di er signi cantly from single atom dynamics due to the phenomenon of Rydberg blockade.
Additionally, the number of excitations in the Rydberg atomic chain depends strongly on
the detuning from resonance which leads to dynamical crystallisation. In the second part we
study an atomic chain embedded in photonic crystal waveguide with atomic frequency highly
detuned from the photonic band edge frequency. Here, due to the presence of band gap, a
coherent hopping of Rydberg excitations takes place in the atomic chain. This coherent
many-body interaction is designed appropriately to facilitate controlled hopping along the
atomic chain which emulates quantum walk dynamics.
