<Time evolution> gives $e^{-iE_0t/\hbar}[\phi_0+e^{-i\omega t}\phi_1]/\sqrt2$. 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.

Solution

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

 Solution (source code)