Atomic coherence decay due to interactions with strong coherent radiation

The time development of $N$ two-level atoms linearly coupled to a monochromatic, long-wavelength radiation field is studied. Both systems are assumed to be initially in coherent states, the radiation mode being strongly populated with an average number $n$ of photons larger than $N$. The decay of atomic coherence can be followed up to a time $t^{*}$, after which the perturbation expansion in powers of $n^{-\frac{1}{2}}$ used to solve the problem breaks down. We show that it increases proportional to $t^2$ at large times, as measured from the variances of the components of the total angular momentum of the atoms. The results are briefly discussed in connection with the problem of conversion of incoherent into coherent radiation.