  In this paper we investigate the quantum and classical dynamics of a single
trapped ion subject to nonlinear kicks derived from a periodic sequence of
Guassian laser pulses. We show that the classical system exhibits diffusive
growth in the energy, or 'heating', while quantum mechanics suppresses this
heating. This system may be realized in current single trapped-ion experiments
with the addition of near-field optics to introduce tightly focussed laser
pulses into the trap.
