Dispersive Jaynes-Cummings Hamiltonian describing a two-level atom interacting with a two-level single mode field

We investigate the time evolution of statistical properties of a single mode radiation field after its interaction with a two-level atom. The entire system is described by a dispersive Jaynes-Cummings Hamiltonian assuming the atomic state evolving from an initial superposition of its excited and ground states, $\mathrm{\mid }e⟩+\mathrm{\mid }g⟩,$ and the field evolving from an initial superposition of two excited levels, $\mathrm{\mid }{n}_1⟩+\mathrm{\mid }{n}_2⟩$. It is found that the field evolution is periodic, the period depending on the ratio $n_2\mathrm{/}{n}_1\mathrm{.}$ The energy excitation oscillates between these two states and the statististics can be either sub- or super-Poissonian, depending on the values $n_1,$ $n_2$.