Simplified landscapes for optimization of shaken lattice interferometry

Motivated by recent results using shaken optical lattices to perform atom interferometry, we explore the 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 +/- 2hk(L) splitting via single-frequency shaking. This is confirmed both via simulation and experiment. Furthermore, we are able to split with a relative phase theta between the two split arms of 0 or pi depending on our shaking frequency. Addressing higher-order splitting, we determine that +/- 6hk(L) splitting is sufficient to be able to accelerate the atoms in counterpropagating lattices. Finally, we show that we can use a genetic algorithm to optimize +/- 4hk(L) and +/- 6hk(L) splitting to with in approximate to 0.1% by restricting our optimization to the resonance frequencies corresponding to single-and two-photon transitions between Bloch bands. As a proof-of-principle, an experimental demonstration of simplified optimization of 4hk(L) splitting is presented.