Gaseous Bose-Einstein condensates (BECs) present unique possibilities as bright, coherent matter wave sources for applications to coherent atom optics, holography and interferometry.  There is much interest in creating novel atom optical elements for focusing and deposition, coupling of atoms with high efficiency into atom chip guides, collimation of atomic trajectories within an atomic clock to suppress systematic effects, and for the exploration of fundamental physics with matter waves.

    However, unlike photonic optics, propagation of matter waves is profoundly affected by the interactions between atoms.  For example, in a gaseous Bose-Einstein condensate, the “mean-field” driven expansion destroys the Heisenberg-limited momentum distribution possessed by a condensate while it is trapped, creating a matter wave with a broad spread of velocities that is undesirable for atom-optical applications.  Therefore, it is of great interest to discover methods of controlling and suppressing interaction effects during propagation of a matter wave field and within atom interferometers.

    We have realized a conical matter wave lens. The repulsive potential of a focused laser beam was used to launch a Bose-Einstein condensate into a radially expanding wavepacket whose perfect ring shape was ensured by energy conservation. In spite of significant interactions between atoms, the spatial and velocity widths of the ring along its radial dimension remained extremely narrow, as also confirmed by numerical simulations.  Our results open the possibility for cylindrical atom optics without the perturbing effect of mean-field interactions.