  We experimentally explore the underlying pseudo-classical phase space
structure of the quantum delta kicked accelerator. This was achieved by
exposing a Bose-Einstein condensate to the spatially corrugated potential
created by pulses of an off-resonant standing light wave. For the first time
quantum accelerator modes were realized in such a system. By utilizing the
narrow momentum distribution of the condensate we were able to observe the
discrete momentum state structure of a quantum accelerator mode and also to
directly measure the size of the structures in the phase space.
