Complete controllability of quantum systems

Complete controllability is a fundamental issue in the field of control of quantum systems because of its implications for dynamical realizability of the kinematical bounds on the optimization of observables. Of special importance is the question of complete controllability of Morse and harmonic oscillators since they serve as basic models for many physical systems. We prove that most non-decomposable, anharmonic quantum systems, including the N-level Morse oscillator, are completely controllable with a single control. Furthermore, we establish sufficient conditions for complete controllability of systems with equally spaced energy levels and show that they are satisfied by the standard N-level harmonic oscillator