Coherence-Like States of Two Coulomb-Correlated Ions Confined in a Paul Trap

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.