JultikaUniversity of Oulu repository

Lattices consisting of cavity QED and circuit QED elements have come under focus as a platform for studying several novel quantum phenomena. In particular, a lattice of Rabi systems described by the Rabi-Hubbard model is expected to display a new Z2 parity symmetry-breaking phase transition of light between a Rabi insulator and a delocalized superradiant phase. In this thesis, we examine a superconducting circuit called the artificial trapped ion as a means to realize a nonlinear Rabi-Hubbard lattice. We use mean field theory and second-order perturbation theory to derive an expression for the boundary of the phase transition and calculate it numerically. We show that nonlinearity in the light-matter coupling results in nontrivial behavior for the phase boundary, in the form of a peak arising at a certain strength of the nonlinearity. We also see a behavior of oscillation followed by saturation as the nonlinearity increases.