Effects of Kerr medium in coupled cavities on quantum state transfer

We study the effect of Kerr type nonlinear medium in quantum state transfer. We have investigated the effect of different coupling schemes and Kerr medium parameters $p$ and $\omega_{{K}}$. We found that, the Kerr medium introduced in the connection channel can act like a controller for quantum state transfer. The numerical simulations are performed without taking the adiabatic approximation. Rotating wave approximation is used in the atom-cavity interaction only in the lower coupling regime.