  We uncover signatures of quantum chaos in the many-body dynamics of a
Bose-Einstein condensate-based quantum ratchet in a toroidal trap. We propose
measures including entanglement, condensate depletion, and spreading over a
fixed basis in many-body Hilbert space which quantitatively identify the region
in which quantum chaotic many-body dynamics occurs, where random matrix theory
is limited or inaccessible. With these tools we show that many-body quantum
chaos is neither highly entangled nor delocalized in the Hilbert space,
contrary to conventionally expected signatures of quantum chaos.
