Quantum lens for atomic waves

We consider the focusing and deflection of a nonresonant atomic beam propagating through a spatially inhomogeneous quantized electromagnetic field. Different Fock states of the field deflect the atoms in different angles and focus them at different points. We find a regime in which individual foci corresponding to neighboring Fock states can be reoslved even for large average number of photons. In this sense this quantum lens for atomic waves leaves intact the discreteness of the photons even in the classical limit