  In this paper, we study, in the semiclassical sense, the global approximate
controllability in small time of the quantum density and quantum momentum of
the 1-D semiclassical cubic Schr\"odinger equation with two controls between
two states with positive quantum densities. We first control the asymptotic
expansions of the zeroth and first order of the physical observables via
Agrachev-Sarychev's method. Then we conclude the proof through techniques of
semiclassical approximation of the nonlinear Schr\"odinger equation.
