Controllability for a coupled system of Schrödinger equations<br/><br/>modeling a trapped ion

Monday, March 2, 2009 - 2:50pm - 3:20pm
EE/CS 3-180
Jean-Pierre Puel (Université Versailles/Saint Quentin-en-Yvelines)
We analyse the possibility of control for a coupled system of
Schrödinger equations on the whole real line for the harmonic
oscillator modeling a single trapped ion. In fact the coupling
is due to the control which acts as a potential and which is
performed by three monochromatic waves which can be switched on
and off, only one of them being active at each time.
By taking the frequency of these waves large enough, we show
that this sytem can be approximated by a much simpler one, the
so-called Law-Eberly system, for which we can give an explicit
control satisfying all requirements. This enables us to prove
approximate controllability for the original system in the
natural (L2)2 norms and also in much stronger norms.
This work has been done in collaboration with Sylvain Ervedoza.
MSC Code: