EVOLUTION OF WAVE-FUNCTIONS IN THE 2-PHOTON JAYNES-CUMMINGS MODEL - THE GENERATION OF SUPERPOSITIONS OF COHERENT STATES

The pure-state evolution of the atomic as well as the field states in the resonant two-photon Jaynes-Cummings model with the field initially in the coherent state is studied. Analytic expressions for various qu antities involved are obtained under the large-($) over bar n approxim ation. It is shown that the atom as well as the field are approximatel y in the pure state for gt = k pi/4, where k is an integer and in a co mpletely pure state for gt = k pi. The field states generated at the t imes gt = k pi/4 are shown to be a quantum superposition of the cohere nt states for a particular choice of the relative phase. The interfere nce between these states leads to a spiked photon-number distribution but the field is still Poissonian.