Abstract
Thorough control of the optical mode of a single photon is essential for quantum information applications. We present a comprehensive experimental and theoretical study of a light-matter interface based on cavity quantum electrodynamics. We identify key parameters like the phases of the involved light fields and demonstrate absolute, flexible, and accurate control of the time-dependent complex-valued wave function of a single photon over several orders of magnitude. This capability will be an important tool for the development of distributed quantum systems with multiple components that interact via photons.