= Weak-pulse Ramsey spectrum
{title2=$P_e=(\Omega\tau)^2\operatorname{sinc}^2(\delta\tau/2)\cos^2(\delta T/2)$}
For two coherent square pulses of equal duration $\tau$, pulse-start separation $T\geq\tau$, resonant <Rabi angular frequency> $\Omega$, and <Rabi detuning> $\delta$, the initially lower-state <transition probability> has the displayed leading weak-excitation form when $|\Omega|\tau\ll1$. Integrating the first-order <probability amplitude> over both windows gives a sum of two equal <Fourier transforms>, with relative <quantum phase> $\delta T$. The factor four from coherent addition makes the central value $(\Omega\tau)^2$. The <rotating-wave approximation> additionally requires many carrier cycles per pulse and near-resonant weak driving.
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