  The metallic tip of a scanning force microscope operated at 300 mK is used to
locally induce a potential in a fully controllable double quantum dot defined
via local anodic oxidation in a GaAs/AlGaAs heterostructure. Using scanning
gate techniques we record spatial images of the current through the sample for
different numbers of electrons on the quantum dots (i.e., for different quantum
states). Owing to the spatial resolution of current maps, we are able to
determine the spatial position of the individual quantum dots, and investigate
their apparent relative shifts due to the voltage applied to a single gate.
