Off-resonant photon scattering (${\Gamma }_{\mathrm{sc}}\sim \Gamma |\Omega {|}^2/(4{\Delta }^2)$)

A detuned optical drive still admixes a decaying excited state. Its spontaneous scattering rate is of order $\Gamma |\Omega {|}^2/(4{\Delta }^2)$ for weak far-detuned driving with coupling $\hslash \Omega /2$. Increasing detuning at fixed optical power reduces both unwanted scattering and useful coherent coupling.