Number theory and matter waves

At Nakagawa-laboratory at The University of Electro-communication, we have performed experiments linking one of number theory's most basic tools - exponential sums - with quantum interference of matter waves.In particular we have investigated factoring using Gauss sums and signal processing with discrete Fourier transforms by carefully controlling the phase of a potential in which a Bose-Einstein condensate of Rubidium is present. In this talk I will present our experimental methods and results.