Effective quantum teleportation of an atomic state between two cavities with the cross-Kerr nonlinearity by interference of polarized photons

In this paper, we propose a protocol for long-distance quantum teleportation of the unknown state of an atom trapped in an optical cavity to a second atom trapped in another distant optical cavity with the help of the cross-Kerr nonlinearity. The setup involves cavities QEDs and linear optical elements, which are feasible with existing experimental technology. More over, in Lame-Dicke limit, the protocol does not require the simultaneous click of the detectors. These make the protocol more realizable in experiments. We also show that the protocol can be successfully realized with a certain probability.