Cumulative Fidelity of LMT Clock Atom Interferometers in the Presence of Laser Noise

Clock atom interferometry is an emerging technique in precision measurements that is particularly well suited for sensitivity enhancement through large momentum transfer (LMT). While current systems have demonstrated momentum separations of several hundreds of photon momenta, next-generation quantum sensors are targeting an LMT enhancement factor beyond $10^4$. However, the viability of LMT clock interferometers has recently come into question due to the potential impact of laser frequency noise. Here, we resolve this concern by analyzing the cumulative fidelity of sequential state inversions in an LMT atom interferometer. We show that the population error from $n$ pulses applied from alternating directions scales linearly with $n$. This is a significant advantage over the $n^2$ scaling that occurs when probing a two-level system $n$ times from the same direction. We further show that contributions to the interferometer signal from parasitic paths generated by imperfect pulses are negligible, for any loss mechanism. These results establish that laser frequency noise is not a practical limitation for the development of high-fidelity LMT clock atom interferometers.