Coherence properties of theN-atom-radiation interaction and the Holstein-Primakoff transformation

We consider a system of N two-level atoms initially in the ground state and interacting with a small [〈n(t=0)〉N] coherent radiation field. The field is assumed to be monochromatic, and its wavelength is taken to be much larger than the dimensions of the region of the N atoms. The statistical properties of both the atomic system and the radiation field are studied as functions of time. Using the Holstein-Primakoff transformation, it is shown that the initial coherence of the system tends to disappear after the energy of the system has been exchanged between atoms and field a number of times approximately given by N/〈n(t=0)〉.