  We investigate the effect of cantori on momentum diffusion in a quantum
system. Ultracold caesium atoms are subjected to a specifically designed
periodically pulsed standing wave. A cantorus separates two chaotic regions of
the classical phase space. Diffusion through the cantorus is classically
predicted. Quantum diffusion is only significant when the classical phase-space
area escaping through the cantorus per period greatly exceeds Planck's
constant. Experimental data and a quantum analysis confirm that the cantori act
as barriers.
