Probing submicron forces by interferometry of Bose-Einstein condensed atoms

We propose a technique, using interferometry of Bose-Einstein condensed alkali atoms, for the detection of submicron-range forces. It may extend present searches at 1 micron by 6 to 9 orders of magnitude, deep into the theoretically interesting regime of 1000 times gravity. We give several examples of both four-dimensional particles (moduli), as well as higher-dimensional particles---vectors and scalars in a large bulk---that could mediate forces accessible by this technique.