Splitting matter waves using an optimized standing-wave light-pulse sequence

In a recent experiment (Wang et al., e-print cond-mat/0407689), it was observed that a sequence of two standing-wave square pulses can split a Bose-Einstein Condensate at rest into ±2ℏk diffraction orders with almost 100% efficiency. By truncating the Raman-Nath equations to a two-state model, we provide an intuitive picture that explains this double-square-pulse beam-splitter scheme. We further show it is possible to optimize a standing-wave multiple-square-pulse sequence to efficiently diffract an atom at rest to a symmetric superposition of ±2nℏk diffraction orders with n>1. The approach is considered to be qualitatively different from the traditional light-pulse schemes in the Bragg or the Raman-Nath region, and can be extended to more complex atomic optical elements that produce various tailored output momentum states from a cold atom source.