  In this paper we develop a unified framework to study the coherent control of
trapped ions subject to state-dependent forces. Taking different limits in our
theory, we can reproduce two different designs of a two-qubit quantum gate
--the pushing gate [1] and the fast gates based on laser pulses from Ref.
[2]--, and propose a new design based on continuous laser beams. We demonstrate
how to simulate Ising Hamiltonians in a many ions setup, and how to create
highly entangled states and induce squeezing. Finally, in a detailed analysis
we identify the physical limits of this technique and study the dependence of
errors on the temperature. [1] J.I. Cirac, P. Zoller, Nature, 404, 579, 2000.
[2] J.J. Garcia-Ripoll, P. Zoller, J.I. Cirac, PRL 67, 062318, 2003
