Preparation of entangled coherent states of the electromagnetic field based on detecting the state of the atom in the Jaynes-Cummings model

We propose a method to generate the entangled quantum states of a field via the nonresonant interaction of a two-level atom with a two-mode field. When the detuning between the atomic transition frequency and the frequency of each mode is much larger than the coupling constant, the photon statistical distribution of the field will not be changed during the interaction of the atom with the field, while the phase of the field will evolve with time. By state-selective measurements on the atom, we can produce the entangled coherent states of the field if the two modes of the field are both in the coherent states initially. Entanglements of other states can also be generated by this method.