= Resonance envelope of a Rabi transition
{title2=$P_{\max}(\delta)=\Omega^2/(\Omega^2+\delta^2)$}
In the <Driven two-level Rabi model>, the transition <probability> is $P(t)=\Omega^2\sin^2(\sqrt{\Omega^2+\delta^2}\,t/2)/(\Omega^2+\delta^2)$. Maximizing over time at each detuning gives a <Lorentzian line shape>, with first maximizing time $\pi/\sqrt{\Omega^2+\delta^2}$ and <full width at half maximum> $2|\Omega|$ in angular frequency. The amplitude parameter $\Omega$ must use the specified <Rabi angular frequency> convention.
This envelope differs from a spectrum obtained with a fixed pulse duration: optimizing the time separately removes the sine-squared factor, while fixing time retains it. A finite linewidth here describes detuning-limited transfer under coherent driving, without requiring dissipative decay.
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