  Using a system consisting of a freely falling cloud of cold cesium atoms
periodically kicked by pulses from a vertical standing wave of laser light, we
present the first experimental observation of high-order quantum accelerator
modes. This confirms the recent prediction by Fishman, Guarneri, and Rebuzzini
[Phys. Rev. Lett. 89, 084101 (2002)]. We also show how these accelerator modes
can be identified with the stable regions of phase space in a classical-like
chaotic system, despite their intrinsically quantum origin.

Atomic Physics;Chaotic Dynamics