### Refine

#### Keywords

- AC-DC-Wannier-Stark systems (1)
- Quantum mechanics (1)
- Wannier-Stark systems (1)
- decay rate (1)
- lifetime statistics (1)
- lifetimes (1)
- nonhermitian perturbation theory (1)
- optical lattices (1)
- resonances (1)

The paper studies the effect of a weak periodic driving on metastable Wannier-Stark states. The decay rate of the ground Wannier-Stark states as a continuous function of the driving frequency is calculated numerically. The theoretical results are compared with experimental data of Wilkinson et at. [Phys.Rev.Lett.76, 4512 (1996)] obtained for cold sodium atoms in an accelerated optical lattice.

We study the transitions between the ground and excited Wannier states induced by a weak ac field. Because the upper Wannier states are several order 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 nonhermitian 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.