Decay of Quantum Correlations in Atom Optics Billiards with Chaotic and Mixed Dynamics

We perform echo spectroscopy on ultra cold atoms in atom optics billiards, to study their quantum dynamics. The detuning of the trapping laser is used to change the ``perturbation'', which causes a decay in the echo coherence. Two different regimes are observed: First, a perturbative regime in which the decay of echo coherence is non-monotonic and partial revivals of coherence are observed. These revivals are more pronounced in traps with mixed dynamics as compared to traps where the dynamics is fully chaotic. Next, for stronger perturbations, the decay becomes monotonic and independent of the strength of the perturbation. In this regime no clear distinction can be made between chaotic traps and traps with mixed dynamics.