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Large-momentum-transfer~(LMT) atom interferometers using elastic Braggscattering on light waves are among the most precise quantum sensors to date.To advance their accuracy from the mrad to the $\mu$rad regime, it is necessaryto understand the rich phenomenology of the Bragg interferometer, which differssignificantly from that of a standard two-mode interferometer. We develop ananalytic model for the interferometer signal and demonstrate its accuracy usingcomprehensive numerical simulations. Our analytic treatment allows thedetermination of the atomic projection noise limit of an LMT Bragginterferometer, and provides the means to saturate this limit. It affordsaccurate knowledge of the systematic phase errors as well as their suppressionby two orders of magnitude down to a few $\mu\mathrm{rad}$ using appropriatelight pulse parameters.

Large-momentum-transfer atom interferometers with $\mu$rad-accuracy using Bragg diffraction