We present new results on the quantum control of systems with infinitely large Hilbert spaces. A control-theoretic analysis of the control of trapped ion quantum states via optical pulses is performed. We demonstrate how resonant bichromatic fields can be applied in two contrasting ways -- one that makes the system completely uncontrollable, and the other that makes the system controllable. In some interesting cases, the Hilbert space of the qubit-harmonic oscillator can be made finite, and the Schr\"{o}dinger equation controllable via bichromatic resonant pulses. Extending this analysis to the quantum states of two ions, a new scheme for producing entangled qubits is discovered.
@article{arxiv.quant-ph/0401032,
title = {Control of trapped-ion quantum states with optical pulses},
author = {C. Rangan and A. M. Bloch and C. Monroe and P. H. Bucksbaum},
journal= {arXiv preprint arXiv:quant-ph/0401032},
year = {2007}
}