On decoherence and nonlinear effects in the generation of quantum states of motion in Paul traps

We study some possible sources of decoherence in the generation of nonclass ical states of motion of ions in Paul traps by means of numerical simulatio ns based on reported experiments. In particular we study the consequences o f the spontaneous decay of the internal energy state \0 > (i) which couples the two hyperfine internal states \1 > (i) and \2 > (i) in the two-photon Raman transitions used to manipulate the ion motional state. We also consid er some possible experimental limitations to generate coherent states due t o nonlinear effects in the coupling of the centre-of-mass coordinates with the laser field. A similar analysis is performed for carrier pulses taking into account nonlinearities and micromotion. The quantum evolution of the i on internal and centre-of-mass degrees of freedom are studied using amplitu de equations derived from Schrodinger's equation. The limitations of such a n approach are also discussed.