  In ion traps, entangling gate operations can be realized by a bichromatic
pair of laser beams that collectively interact with the ions. In this paper, a
new method of modelling the laser-ion interaction is introduced that turns out
to be superior to standard techniques for the description of gate operations on
optical qubits. The treatment allows for a comparison of the performance of
gates based on $\sigma_z\otimes\sigma_z$ and M{\o}lmer-S{\o}rensen interactions
on optical transitions where the bichromatic laser field can be realized by an
amplitude-modulated laser resonant with the qubit transition. Shaping the
amplitude of the bichromatic laser pulse is shown to make the gates more robust
against experimental imperfections.
