Localized Single-Photon Wave Functions in Free Space

Abstract
We solve the joint open problems of photon localization and single-photon wave functions in the context of spontaneous emission from an excited atom in free space. Our wave functions are well-defined members of a discrete orthonormal function set. Both the degree and shape of the localization are controlled by entanglement mapping onto the atom wave function, even though the atom is remote from the photon.