Abstract
We describe the measurement and compensation of optical Stark shifts induced by an off-resonant pulse for manipulating the terahertz-separated states $3\text{ }{^{2}D}_{3/2}--3\text{ }{^{2}D}_{5/2}$, in a single trapped ${^{40}\text{C}\text{a}}^{+}$ ion. These states can be used as a quantum bit and are coupled by a two-photon stimulated Raman transition with phase-locked light sources bridged by an optical comb generator. The induced optical Stark shift is measured by Ramsey interferometry. We estimate the power ratio of Raman beams that cancel the level shift with an uncertainty of 170 Hz. A shift of the same amount as this uncertainty is estimated to give rise to an infidelity of approximately $7.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ during a $\ensuremath{\pi}/2$ rotation operation.
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