Induced transitions between Wannier ladders

We study the transitions between the ground and excited Wannier states indu ced 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 probabilit y leakage or decay rate. Using non-Hermitian resonant perturbation theory w e obtain an analytical expression for this induced decay rate. The analytic al results are compared with exact numerical calculations of the system dec ay rate.