= Equatorial reachability of a detuned spin pulse
{title2=$|\Delta|\leq\Omega$}
For an initial pole of the <Bloch sphere>, one fixed-amplitude harmonic pulse detuned by $\Delta$ transfers at most $\Omega^2/(\Omega^2+\Delta^2)$ of the population. A pure equatorial state requires half transfer, so some pulse duration reaches the equator exactly when $|\Delta|\leq\Omega$. Adjusting drive <phase> then selects its transverse azimuth. Exact inversion to the opposite pole is unavailable for nonzero detuning with that single fixed pulse. This is a restriction on the specified controls, rather than on composite-pulse or frequency-swept state preparation.
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