Quantum instability in cavity QED

The stability and instability of quantum evolution are analyzed in the interaction of a two-level atom with a quantized-field mode in an ideal cavity with allowance for photon recoil, which is the basic model of cavity QED. It is shown that the Jaynes-Cammings quantum dynamics can be unstable in the regime of the random walk of the atom in the quantized field of a standing wave in the absence of any interaction with the environment. This instability is manifested in large fluctuations of the quantum entropy, which correlate with a classical-chaos measure, the maximum Lyapunov exponent, and in the exponential sensitivity of the fidelity of the quantum states of the strongly coupled atom-field system to small variations of resonance detuning. Numerical experiments reveal the sensitivity of the atomic population inversion to the initial conditions and to correlation between the quantum and classical degrees of freedom of the atom.