Search

We report the n×n' coherence-like state solutions in the cases of n,n' = 1,2,... for the system including two Coulomb-correlated ions confined in a one-dimensional Paul trap with a time-dependent harmonic potential. One of the n' exact solutions of the centre-of-mass motion describes a generalized coherent state. For a small driving strength the n approximate solutions of relative motion are constructed, which describe the coherent oscillations of the two ions around the classical equilibrium position.

We investigate the regular and chaotic motions of a single Paul-trapped ion under the pseudopotential approximation, which interacts with a double-δ-kicked periodic potential. We apply the method of integral-equation to construct the exact solution of the classical equation and use the numerical technique to plot the orbits in phase space and the time evolutions of average energies. Combining the analytical results with the numerical ones, we arrived at two interesting conclusions: Firstly, there are regular stable motions of the double δ-kicked system,at variance with the resonance case of the corresponding single δ-Kicked system. Secondly, when the time interval between the double δ pulses becomes shorter, the regular motion of the system becomes chaotic, and the speed of classical diffusion of the average energy is related to the degree of chaos. It is shown that the resonance may lead to loss of stability and the instability can be controlled by adjusting the laser wave vector.

Under the pseudopotential approximation, for a single Paul trapped ion which interacts with a flashing ratchet potential formed by two laser standing waves, we apply the method of integral-equation to construct the exact solution of the classical equation, and use the numerical technique to plot the orbits in phase space and calculate the current defined by the average velocity. By combining the analytical results with numerical ones,we investigate the regular and chaotic motions of the system. Compared to the case of the flashing lattice potential, two important ratchet effects are found here: First, the flashing ratchet potential changes the chaotic region in the parameter space such that we can make the regular motion of ion chaotic or vice versa by adjusting the parameters of the second laser. Secondly, by analyzing the evolutions of the average current versus the laser parameters, we find that the presence of the flashing ratchet potential can lead the trapped ion to be transported in averagy along a single direction. When the potential strength is increased to the chaotic region, the current decreases evidently and its direction varies, indicating the onset of chaotic motion.