A single-photon large-momentum-transfer atom interferometry scheme for Sr or Yb atoms with application to determining the fine-structure constant

The leading experimental determinations of the fine-structure constant, $\alpha$, currently rely on atomic photon-recoil measurements from Ramsey-Bord\'e atom interferometry with large momentum transfer to provide an absolute mass measurement. We propose an experimental scheme for an intermediate-scale differential atom interferometer to measure the photon-recoil of neutral atomic species with a single-photon optical clock transition. We calculate trajectories for our scheme that optimise the recoil phase while nullifying the undesired gravity-gradient phase by considering independently launching two clouds of ultracold atoms with the appropriate initial conditions. For Sr and Yb, we find an atom interferometer of height 3m to be sufficient for an absolute mass measurement precision of $\Delta m / m \sim 1\times 10^{-11}$ with current technology. Such a precise measurement (the first of its kind for Sr or Yb) would halve the uncertainty in $\alpha$ -- an uncertainty that would no longer be limited by an absolute mass measurement. The removal of this limitation would allow the uncertainty in $\alpha$ to be reduced by a factor of 10 by corresponding improvements in relative mass measurements, thus paving the way for higher-precision tests of the Standard Model of particle physics.