The
quantum dynamics of ultra-cold atoms inside dark optical traps (known
as
"atom-optics billiards") is studied using a new spectroscopic
technique. In
an experimental realization of a "gedanken experiment" proposed by
Asher
Peres in 1984 [Phys. Rev. A30, 1610] the decay of quantum correlations
of
perturbed high-lying states (with <n> up to 10^8) are measured
when the
underlying classical motion is regular, chaotic or mixed. For weak
perturbations we observe partial quantum revivals, reflecting
non-universal
features of the perturbation and for strong perturbations we observe a
regime where the correlation decay times are independent in the
perturbation
strength.