Jaynes-Cummings collapse and revival ($t_{\mathrm{rev}}\simeq 2\pi \sqrt{\bar{n}}/g$)

An initially excited atom interacting resonantly with a coherent state has inversion ${\sum }_n{P}_n\cos (2g\sqrt{n+1}t)$, where $P_n$ is its Poisson distribution of photon number. Different Rabi frequencies dephase on a time scale $1/g$ and approximately rephase near $2\pi \sqrt{\bar{n}}/g$. The revival estimate follows from the adjacent-component frequency difference $g/\sqrt{\bar{n}}$. Large mean photon number makes the early oscillations nearly classical without removing the discrete spectrum responsible for revivals.