  Favored schemes for trapped-ion quantum logic gates use bichromatic laser
fields to couple internal qubit states with external motion through a
"spin-dependent force." We introduce a new degree of freedom in this coupling
that reduces its sensitivity to phase decoherence. We demonstrate bichromatic
spin-dependent forces on a single trapped $^{111}$Cd$^+$ ion, and show that
phase coherence of the resulting "Schr\"{o}dinger-cat" states of motion depends
critically upon the spectral arrangement of the optical fields. This applies
directly to the operation of entangling gates on multiple ions.
