Detection-resolution limits of large-momentum-transfer atom gravimetry

Large momentum transfer (LMT) enhances the gravitational phase of a light-pulse atom interferometer by a factor $n$, while mirrorless operation with momentum-resolved detection can quadruple the phase-carrying quantum Fisher information. These gains compete in practice because the momentum-space fringe period scales as $1\mathrm{/}n$, making the fringe signal increasingly vulnerable to finite detector resolution. We analyze this trade-off in a solvable model with instantaneous lossless $n$-photon pulses, a Gaussian source, and Gaussian detection blur, allowing continuous interpolation between Kasevich–Chu and mirrorless geometries. Closed-form expressions for the blurred output distributions and classical Fisher information are obtained, with a fringe-phase averaging approximation whose error is exponentially suppressed and agrees with numerical simulations at the ${10}^{-8}$ level. We find that mirrorless operation surpasses a conventional interferometer with the same momentum transfer only when ${\sigma }_p<0.91m\mathrm{/}(n{k}_{0}T)$. Fringe-based readout exhibits an optimal momentum transfer $n^{\ast }\simeq 0.93m\mathrm{/}({\sigma }_p{k}_{0}T)$ and a resolution-limited sensitivity floor $\mathrm{\Delta }g\simeq 4.4{\sigma }_p\mathrm{/}(mT\sqrt{N})$, independent of photon momentum. When this criterion is not satisfied, partial mirror asymmetry can recover part of the enhancement, whereas population-based readout remains insensitive to detector blur and ultimately favors the conventional sequence at sufficiently large $n$. Estimates for ${}^{87}$Rb sensors show that the mirrorless advantage is primarily restricted to short-baseline instruments.