Nonexponential Decoherence and Momentum Subdiffusion in a Quantum Lévy Kicked Rotator

We investigate decoherence in the quantum kicked rotator (modeling cold atoms in a pulsed optical field) subjected to noise with power-law tail waiting-time distributions of variable exponent (Lévy noise). We demonstrate the existence of a regime of nonexponential decoherence where the notion of a decoherence rate is ill defined. In this regime, dynamical localization is never fully destroyed, indicating that the dynamics of the quantum system never reaches the classical limit. We show that this leads to quantum subdiffusion of the momentum, which should be observable in an experiment.

Figure 1

Time dependence of the momentum spreading $\mathrm{var}p(t)$ for kicked rotators which are subjected to Lévy noise generated by a Yule-Simon distribution. The results of numerical simulations (solid curves) are compared to the theoretical predictions from Eq. (4) (dashed curves). The straight solid line shows the classical diffusive momentum spreading. In the upper panel, the exponent $\alpha$ varies while the noise strength $\kappa =1/300$ is fixed. The bottom panel shows results for fixed $\alpha =0.5$ and varying noise strength $\kappa$.