  We investigate the dephasing of ultra cold ^{85}Rb atoms trapped in an
optical dipole trap and prepared in a coherent superposition of their two
hyperfine ground states by interaction with a microwave pulse. We demonstrate
that the dephasing, measured as the Ramsey fringe contrast, can be reversed by
stimulating a coherence echo with a pi-pulse between the two pi/2 pulses, in
analogy to the photon echo. We also demonstrate that the failure of the echo
for certain trap parameters is due to dynamics in the trap, and thereby that
''echo spectroscopy'' can be used to study the quantum dynamics in the trap
even when more than 10^6 states are thermally populated, and to study the
crossover from quantum (where dynamical decoherence is supressed) to classical
dynamics.

Quantum Physics;Chaotic Dynamics;Atomic Physics