Simulation of Three-Spin Interaction in Coupled Cavities Chain

We generalize usual second-order effective Hamiltonian approximation into third-order. Employing the generalized method, we propose a scheme to generate three-spin interaction using coupled cavity chain. We show that the third order term not only improves two parties interaction but also induces direct three-spin interaction which has not been simulated before. By controlling the frequency of laser field, one can obtain next nearest neighbor interaction on the same order with the nearest neighbor’s or the three-spin interaction on the same order as next nearest neighbor’s.