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.
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