A fast and accurate method for simulating Bragg atom interferometers

Atom interferometers are used in a variety of applications, from measuring gravity and gravity gradients in the field to performing tests of fundamental physics in the lab. One method of increasing interferometer sensitivity is to produce a larger momentum difference between interferometer arms through the use of large momentum transfer methods, such as Bragg diffraction. However, Bragg diffraction introduces systematic effects in the accumulated interferometer phase that are challenging to characterize. A Bragg atom interferometer is described by the one-dimensional time-dependent Schr\"odinger equation (1D-TDSE). In this paper we show that for the case of Bragg diffraction the 1D-TDSE partial differential equation can be separated into several systems of ordinary differential equations, allowing for the use of adaptive step size Runge-Kutta methods. We compare the convergence of this method to the split-step and Crank-Nicolson methods, and present a method for further computational speed-ups using a lookup table.