= Identical-pulse Ramsey return probability
{title2=$P_{\rm return}=\sin^2(\delta T/2)$}
For ideal identical $R_x(\pi/2)$ pulses separated by $R_z(-\delta T)$, multiply the <unitary operators> to obtain $U=-i[\cos(\delta T/2)X-\sin(\delta T/2)Z]$. An input at either pole of the <Bloch sphere> returns to that same pole with probability $\sin^2(\delta T/2)$. In particular zero delay gives a full NOT, so its return probability is zero. Opposite-sign pulses instead give $\cos^2(\delta T/2)$. The distinction matters when identifying the measured <quantum state population>.
Back to article page
