Robust Optimized Pulse Schemes for Atomic Fountain Interferometry

The robustness of an atomic fountain interferometer with respect to variations in the initial velocity of the atoms and deviations from the optimal pulse amplitude is examined. We numerically simulate the dynamics of an interferometer in momentum space with a maximum separation of $20 \hbar k$ and map out the expected signal contrast depending on the variance of the initial velocity distribution and the value of the laser field amplitude. We show that an excitation scheme based on rapid adiabatic passage significantly enhances the expected signal contrast compared to the commonly used scheme consisting of a series of Rabi pulses. We demonstrate further substantial increase of the robustness by using optimal control theory to identify splitting and swapping pulses that perform well on an ensemble average of pulse amplitudes and velocities. Our results demonstrate the ability of optimal control to significantly enhance future implementations of atomic fountain interferometry.