On the control by electromagnetic fields of quantum systems with   infinite dimensional Hilbert space
  We analyze the control by electromagnetic fields of quantum systems with infinite dimensional Hilbert space and a discrete spectrum. Based on recent mathematical results, we rigorously show under which conditions such a system can be approximated in a finite dimensional Hilbert space. For a given threshold error, we estimate this finite dimension in terms of the used control field. As illustrative examples, we consider the cases of a rigid rotor and of a harmonic oscillator. 
Elie Ass\'emat (ICB), Thomas Chambrion (IECL, INRIA Nancy - Grand Est   / IECN / LMAM), Dominique Sugny (ICB)
math.OC quant-ph