Coherent Control of Dressed Matter Waves

We demonstrate experimentally that matter waves can be coherently and adiabatically loaded and controlled in one-, two-, and three-dimensional strongly driven optical lattices. This coherent control is then used in order to reversibly induce the superfluid-Mott insulator phase transition by changing the strength of the driving. Our findings pave the way for studies of driven quantum systems and new methods for controlling matter waves.