  Bessel beams are plane waves with amplitude profiles described by Bessel
functions. They are important because of their property of limited diffraction
and their capacity to carry orbital angular momentum. Here we report the
creation of a Bessel beam of de Broglie matter waves. The Bessel beam is
produced by the free evolution of a thin toroidal atomic Bose-Einstein
condensate (BEC) which has been set into rotational motion. By attempting to
stir it at different rotation rates, we show that the toroidal BEC can only be
made to rotate at discrete, equally-spaced frequencies, demonstrating that
circulation is quantized in atomic BECs. The method used here to generate
matter wave Bessel beams with a Painted Potential can be viewed as a form of
wavefunction engineering which might be extended to implement arbitrary cold
atom matter wave holography.
