Simplified landscapes for optimization of shaken lattice interferometry

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 $\pm2\hbar k_$\mathrm{L}$$ splitting via single-frequency shaking. This is confirmed both via simulation and experiment. Furthermore, we are able to split with a relative phase $\theta$ between the two split arms of $0$ or $\pi$ depending on our shaking frequency. Addressing higher-order splitting, we determine that $\pm 6\mathrm{\hslash }{k}_{\mathrm{L}}$ splitting is sufficient to be able to accelerate the atoms in counter-propagating lattices. Finally, we show that we can use a genetic algorithm to optimize $\pm 4\mathrm{\hslash }{k}_{\mathrm{L}}$ and $\pm6\hbar k_$\mathrm{L}$$splittingtowithin$\approx0.1%$ by restricting our optimization to the resonance frequencies corresponding to single- and two-photon transitions between Bloch bands.