= Laboratory phase of a resonant spin pulse
{title2=$\varphi_{\rm end}=\varphi+\omega_0\tau$}
With $H_0=-\hbar\omega_0\sigma_z/2$ and a co-rotating transverse magnetic drive of <phase> $\varphi$, an initial spin-up state becomes, up to common <phase>, $\cos(\Omega\tau/2)|\uparrow\rangle+i e^{-i(\varphi+\omega_0\tau)}\sin(\Omega\tau/2)|\downarrow\rangle$. A quarter-turn pulse therefore prepares laboratory $+x$ when $\varphi_{\rm end}=\pi/2$ and $+y$ when $\varphi_{\rm end}=0$. Dropping the free-precession <phase> instead specifies targets in rotating axes. Transverse laboratory targets subsequently precess if the static field is retained.
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