Driven optical lattices as strong-field simulators

We argue that ultracold atoms in strongly shaken optical lattices can be subjected to conditions similar to those experienced by electrons in laser-irradiated crystalline solids, but without introducing secondary polarization effects. As a consequence one can induce nonperturbative multiphoton-like resonances due to the mutual penetration of ac-Stark-shifted Bloch bands. These phenomena can be detected with a combination of currently available laboratory techniques.