  We implement a two-qubit entangling M{\o}lmer-S{\o}rensen interaction by
transporting two co-trapped $^{40}\mathrm{Ca}^{+}$ ions through a stationary,
bichromatic optical beam within a surface-electrode Paul trap. We describe a
procedure for achieving a constant Doppler shift during the transport which
uses fine temporal adjustment of the moving confinement potential. The fixed
interaction duration of the ions transported through the laser beam as well as
the dynamically changing ac Stark shift require alterations to the calibration
procedures used for a stationary gate. We use the interaction to produce Bell
states with fidelities commensurate to those of stationary gates performed in
the same system. This result establishes the feasibility of actively
incorporating ion transport into quantum information entangling operations.
