  We consider a quantum particle in a potential V (x) (x in R^N) subject to a
(spatially homogeneous) time-dependent electric field E(t), which plays the
role of the control. Under generic assumptions on V, this system is
approximately controllable on the L2(R^N;C)-sphere, in su ffiently large times
T, 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 T.
