= Solution
For $\bar n=|z|^2\gg1$, the <Poisson distribution> of <photon number> has width $\sqrt{\bar n}\ll\bar n$. Initially the atom therefore undergoes nearly classical <Rabi oscillations> at <angular frequency> approximately $2g\sqrt{\bar n}$. However, the atomic inversion is a sum over slightly different <frequencies>:
$$
\langle\sigma_z(t)\rangle=\sum_{n=0}^\infty e^{-\bar n}\frac{\bar n^n}{n!}\cos(2g\sqrt{n+1}\,t).
$$
The components dephase, causing collapse of the visible <Rabi oscillations> on a time scale of order $1/g$; a Gaussian photon-number approximation gives an initial envelope approximately $e^{-g^2t^2/2}$. Their discrete <phases> later rephase, giving revivals near
$$
\boxed{t_{\mathrm{rev}}\simeq\frac{2\pi\sqrt{\bar n}}g.}
$$
The revival estimate follows by requiring the <phase> difference of neighbouring photon-number components to advance by $2\pi$. These <Jaynes-Cummings collapse and revival> effects arise from atom-field <entanglement> and photon-number discreteness. Large <amplitude> makes the initial classical description accurate over many Rabi periods, but does not eliminate quantum collapse and revival at all later times.
\Image[/past-exam-of-the-laser-science-and-quantum-information-processing-course-of-the-university-of-oxford/2018-rabi-collapse-and-revival.png]
{title=<Jaynes-Cummings collapse and revival> for a large-amplitude <coherent state>}
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