Atom interferometry, microscopy, complementarity, and the perfect lens*

Development of the `perfect lens' poses an interesting challenge to standard concepts of complementarity manifested in interferometric which-way vs fringe visibility experiments. We show that a `microscope' with a `perfect lens' provides the extremal point of maximum which-way information in atom interferometry, and our theory rigorously connects complementarity in interferometry with the standard position-momentum Heisenberg uncertainty relation.