Photon occupation enhancement of emission (${\Gamma }_{\mathrm{em}}\propto n+1$)

The creation-operator matrix element $⟨n+1|a^{†}|n⟩=\sqrt{n+1}$ makes emission into a radiation mode proportional to $n+1$. The $n$ part is stimulated emission and the remaining part is spontaneous emission. Absorption has the corresponding occupation factor $n$.