Controlling dark solitons on the healing length scale

While usually the optical diffraction limit is setting a limit for the lengthscales on which a typical alkali Bose–Einstein condensate can be controlled, we show that in certain situations control via matter waves can achieve smaller resolutions. For this we consider a small number of impurity atoms which are trapped inside the density dip of a dark soliton state and show that any grey soliton state can be obtained by selectively driving the impurity atoms. This allows to fully control the position and velocity of the dark soliton, and also study controlled collisions between these non-linear objects.