Phase transition and dynamics of qubits in coupled-cavity arrays with nonlinear topological photonics

The topological properties of a coupled-cavity array corresponding to a Su–Schrieffer–Heeger (SSH) model have been investigated through the evolution of a edge cavity, with the Kerr-like nonlinearities added to the inter-cavity coupling strengths. In the topological phase, the state distribution is more localized at the first cavity with the nonlinearities enhanced. The phase transition occurs with the enhancement of nonlinearities after the system evolving for long time when the SSH model is initially at the phase-transition point or in the trivial phase. The entanglement dynamics of two atoms placed in the two edge cavities is explored, and it is found the coupled-cavity array with nonlinearities is more robust against the disturbance of the frequency of each cavity. Moreover, the dynamics and phase transition of a 2-dimensional kagome lattice with the Kerr-like nonlinearities is also discussed through the probability amplitude of the first site after evolving for long time.