High efficiency symmetric beam splitter for cold atoms with a standing wave light pulse sequence

In a recent experiment [1], it was observed that a sequence of two standing wave square pulses can split a BEC at rest into +/- 2 h_bar k diffraction orders with almost 100% efficiency. By truncating the Raman-Nath equations to a 2-state model, we provide an intuitive picture that explains this double square pulse beamsplitter scheme. We further show it is possible to optimize a standingwave multi square pulse sequence to efficiently diffract an atom at rest to symmetric superposition of +/- 2n h_bar k diffraction order 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.