Past exam of the laser science and quantum information processing course of the University of Oxford / 2021 / 3 / b / ii

At resonance, the Hamiltonian operator becomes $\hslash V{\sigma }_x/2$. ThereforeIt gives the requested positive rotation about the x-axis. In the ordered basis $(|1⟩,|0⟩)$, $|1⟩$ becomes $(|1⟩-i|0⟩)/\sqrt{2}$, whose Bloch vector is $(0,-1,0)$.