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Favored schemes for trapped-ion quantum logic gates use bichromatic laserfields to couple internal qubit states with external motion through a"spin-dependent force." We introduce a new degree of freedom in this couplingthat reduces its sensitivity to phase decoherence. We demonstrate bichromaticspin-dependent forces on a single trapped $^{111}$Cd$^+$ ion, and show thatphase coherence of the resulting "Schr\"{o}dinger-cat" states of motion dependscritically upon the spectral arrangement of the optical fields. This appliesdirectly to the operation of entangling gates on multiple ions.Comment: 5 pages, 4 figure

Spin-Dependent Forces on Trapped Ions for Phase-Stable Quantum Gates and Entangled States of Spin and Motion