Diffractive focusing of a uniform Bose-Einstein condensate

The standard way to control the position and the strength of maximal focusing of a matter-wave is to use a lens which imprints a position-dependent phase on the initial wave. However, quantum mechanics allows focusing even without a lens [1,2], based on diffractive focusing, where the initial wave function is a real-valued one with a non-Gaussian shape. Hence, the problem of optimal focusing translates into finding an appropriate initial wave function [3].

We explore the phenomenon of diffractive focusing of an atomic Bose-Einstein condensate in the regime, where the atom-atom interaction plays a key role [4]. We furthermore extend this approach by using attractive interaction to obtain a non-expanding condensate confined solely by its own interaction potential.