Motivated by recent results using shaken optical lattices to perform atom
interferometry, we explore splitting of an atom cloud trapped in a
phase-modulated ("shaken") optical lattice. Using a simple analytic model we
are able to show that we can obtain the simplest case of ±2ℏkL splitting via single-frequency shaking. This is confirmed both
via simulation and experiment. Furthermore, we are able to split with a
relative phase θ between the two split arms of 0 or π depending on
our shaking frequency. Addressing higher-order splitting, we determine that
±6ℏkL splitting is sufficient to be able to accelerate the
atoms in counter-propagating lattices. Finally, we show that we can use a
genetic algorithm to optimize ±4ℏkL and ±6ℏkL splitting to within ≈0.1% by restricting our
optimization to the resonance frequencies corresponding to single- and
two-photon transitions between Bloch bands