The effect of pure decoherence on the Jaynes-Cummings model

We have shown that the Jaynes-Cummings model (JCM) with an environment-induced pure decoherence is an exactly solvable problem. Rabi oscillation of atomic population inversion and oscillation in the field population get trapped due to decoherence. But the decay of the coherence properties of the atom as well as of the held is comparatively slower than that of the population terms. It is also shown that although the fast oscillation in nonclassical properties are suppressed due to decoherence but an initial Poissonian field acquires a sub-Poissonian character in the steady state. So unlike the ordinary spontaneous emission all the nonclassical properties of the system are not erased.