Pulse Schemes for Robust Atomic Fountain Interferometry

Atomic Fountain Interferometry is the state-of-the-art technology for the measurement of gravitational gradients and accelerations with unprecedented precision. It operates by launching a cloud of atoms into a free-fall-tower, using laser pulses acting as the equivalent of beamsplitters and mirrors to separate the cloud into a superposition of two momentum space pathways. However, signal contrast is limited by variations in the initial velocity of the atoms in the cloud and variations in the laser amplitude over the cross-section of the cloud. An ideal, robust pulse scheme must implement separation, mirroring, and recombination of the atoms to high precision over a realistic range of these variations. Here, we analyze the robustness of analytic pulse schemes, starting with the predominantly used sequence of Rabi pulses. We show that using rapid adiabatic passage as an alternative analytical pulse scheme leads to a significant improvement in robustness. Going beyond analytical schemes, we explore numerical optimal control theory to generate robust pulse schemes. We formulate the most general control conditions for the implementation of an interferometer. This allows us to show how phase errors induced by the variations in the Hamiltonian for different atoms in the cloud may be mitigated. We conclude by comparing the robustness of numerical control schemes with the best analytic schemes.