Boscain, UgoMason, Paolo2005-06-202011-09-072005-06-202011-09-072005-06-20Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. 44th IEEE Conference onOPAC Link;http://ieeexplore.ieee.org/servlet/opac?punumber=10559https://openscience.sissa.it/handle/1963/1688On a two-level quantum system driven by an external field, we consider the population transfer problem from the first to the second level, minimizing the time of transfer, with bounded field amplitude. On the Bloch sphere (i.e. after a suitable Hopf projection), this problem can be attacked with techniques of optimal syntheses on 2-D manifolds.136766 bytesapplication/pdfen-USPreprint