Laser Controlling Wavepacket Trains of a Paul Trapped Ion

We have studied the quantum and classical motions of a single Paultrapped ion interacting with a time-periodic laser field. By usingthe test-function method, we construct n exact solutions of quantum dynamics that describe the generalized squeezed coherent states with the expectation orbits being the correspondingclassical ones. The space-time evolutions of the exact probabilitydensities show some wavepacket trains. It is demonstrated analytically that by adjusting the laser intensity and frequency, we can control the center motions of the wavepacket trains. Wealso discuss the other physical properties such as the expectationvalue of energy, the widths and heights of the wavepackets, andthe resonance loss of stability.