Laser controlled quantum motion of two Paul trapped ions

We investigate the quantum motion of two ions stored in a Paul trap and interactingwith a time-periodic laser field. In the pseudopotential approximation and largedetuning condition, we find that the relative motion is independent of the laserfield, but the exact centre-of-mass motion is closely related to the laser field. Byadjusting the laser intensity and frequency, we can well control the quantum motionof the centre-of-mass. We illustrate some physical properties described by thecentre-of-mass states, such as the squeezed coherent property, the widths andheights of the wavepackets of probability density, the classical-quantumcorrespondence, the resonance ladders of expectation energy and the transitionprobabilities between time-dependent quantum levels.