Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2016 / S3 / 2 / e / Solution

Time evolution gives $e^{-i{E}_{0}t/\hslash }[{\varphi }_0+e^{-i\omega t}{\varphi }_1]/\sqrt{2}$. It becomes the opposite relative-sign superposition when $e^{-i\omega t}=-1$, first at $\boxed{t_{\min }=\pi /\omega }$. The overlap with the initial state is proportional to $1+e^{-i\omega t}$ and vanishes then; global phase is immaterial.