Laboratory phase of a resonant spin pulse (${\phi }_{\mathrm{end}}=\phi +{\omega }_0\tau$)

With $H_0=-\hslash {\omega }_0{\sigma }_z/2$ and a co-rotating transverse magnetic drive of phase $\phi$, an initial spin-up state becomes, up to common phase, $\cos (\Omega \tau /2)|\uparrow ⟩+i{e}^{-i(\phi +{\omega }_0\tau )}\sin (\Omega \tau /2)|\downarrow ⟩$. A quarter-turn pulse therefore prepares laboratory $+x$ when ${\phi }_{\mathrm{end}}=\pi /2$ and $+y$ when ${\phi }_{\mathrm{end}}=0$. Dropping the free-precession phase instead specifies targets in rotating axes. Transverse laboratory targets subsequently precess if the static field is retained.