We propose a scheme to enable a controllable cross-Kerr interaction between microwave photons in a circuit quantum electrodynamics （QED） system. In this scheme we use two transmission-line resonators （TLRs） and one superconducting quantum interference device （SQUID） type charge qubit, which acts as an artificial atom. It is shown that in the dispersive regime of the eircuit-QED system, a controllable cross-Kerr interaction can be obtained by properly preparing the initial state of the qubit, and a large cross-phase shift between two microwave fields in the two TLRs can then be reached. Based on this cross-Kerr interaction, we show how to create a macroscopic entangled state between the two TLRs.
This paper introduces two types of two-mode excited entangled coherent states （TMEECSs） ψ±（（α,m,n））, studies their entanglement characteristics, and investigates the influence of photon excitations on quantum entanglement. It shows that for the state （ψ＋ （α, m, m）} the two-mode photon excitations affect seriously entanglement character while the state [ ψ-（α, m, m）） is always a maximally entangled state, and shows how such states can be produced by using cavity quantum electrodynamics and quantum measurements. It finds that the entanglement amount of the TMEECSs is larger than that of the single-mode excited entangled coherent states with the same photon excitation number.
