Past exam of the advanced quantum physics course of the University of Cambridge / 2015 / Paper 1 / 4 / ii

The $+y$ eigenstate is $|+y⟩=(|\uparrow ⟩+i|\downarrow ⟩)/\sqrt{2}$, with ${\sigma }_y(1,i{)}^T=(1,i{)}^T$. Use the same duration ${\tau }_{\pi /2}=\pi /(2\Omega )$ but phaseThe relative amplitude is now $i$, givingThe two transverse preparations differ by a quarter-cycle of RF phase, not by changing the pulse area. Reversing the desired transverse direction adds $\pi$ to the chosen phase.