Induced transitions between Wannier ladders

We study the transitions between the ground and excited Wannier states induced by a weak ac held. Because the upper Wannier states are several orders of magnitude less stable than the ground states, these transitions decrease the global stability of the system characterized by the rate of probability leakage or decay rate. Using non-Hermitian resonant perturbation theory we obtain an analytical expression for this induced decay rate. The analytical results are compared with exact numerical calculations of the system decay rate.