consider a quantum particle in a potential subject to a
(spatially homogeneous) time-dependent electric field, which plays the
role of the control. Under generic assumptions on the potential, this
system is approximately controllable, as proved by Boscain, Caponigro,
Chambrion and Sigalotti. In the present article, we show that this
approximate controllability result is false in small time. As a
consequence, the result by Boscain et al. is, in some sense, optimal
with respect to the control time.