  The stability and instability of quantum motion is studied in the context of
cavity quantum electrodynamics (QED). It is shown that the Jaynes-Cummings
dynamics can be unstable in the regime of chaotic walking of an atom in the
quantized field of a standing wave in the absence of any other interaction with
environment. This quantum instability manifests itself in strong variations of
quantum purity and entropy and in exponential sensitivity of fidelity of
quantum states to small variations in the atom-field detuning. It is quantified
in terms of the respective classical maximal Lyapunov exponent that can be
estimated in appropriate in-out experiments.
