Reversible Destruction of Dynamical Localization

Dynamical localization is a localization phenomenon taking place, for example, in the quantum periodically driven kicked rotor. It is due to subtle quantum destructive interferences and is thus of intrinsic quantum origin. It has been shown that deviation from strict periodicity in the driving rapidly destroys dynamical localization. We report experimental results showing that this destruction is partially reversible when the deterministic perturbation that destroyed it is slowly reversed. We also provide an explanation for the partial character of the reversibility.

Figure 1

Experimentally measured velocity distributions as a function of time. The atomic velocity is measured in units of the recoil velocity $v_r=\hslash k_L/M\simeq 3.5\mathrm{mm}/\mathrm{s}$. At short times, the diffusive broadening (or the reduction of the zero-velocity population) of the velocity distribution is observed. When the slowly changing perturbation is reversed (around $t=17$), the velocity distribution starts to shrink. This is highly nontrivial behavior, showing that the destruction of dynamical localization by a slowly time-varying kick sequence is reversible. After a second cycle of the perturbation a second relocalization of the velocity distribution is observed (around $t=70$).

Figure 2

Upper frame: kick sequence. Main frame: Population in the zero-velocity class as a function of the duration $N$ of the pulse sequence with no resonant light (crossed solid line) and with a $50\mu \mathrm{W}$ pulse of resonant light applied at $t=17$ (dashed line). The absence of revival in the presence of resonant light (decoherence) is a clear-cut proof of the importance of quantum interference for the reversibility of the DL destruction. The inset (a) shows the Gaussian velocity distribution at $t=17$, near the maximum of the perturbation, in the absence of resonant light; inset (b) shows an exponential shape near the minimum of the perturbation, $t=35$.