Coherent and Incoherent Light Scattering by Single-Atom Wave Packets

We study light scattering of atomic wave packets in free space and discuss the results in terms of atom-photon entanglement and which-way information. Using ultracold atoms released from an optical lattice, we realize a Gedanken experiment which interferes single photons scattering off of Heisenberg uncertainty-limited wave packets. We unify the free-space and trapped-atom pictures by measuring the light scattered before and during wave packet expansion and show the coherence properties of the scattered light are independent of the presence of the trap. Therefore, recoilless scattering in a trap (Mössbauer effect), the different frequency of sidebands, and the excitation of an excited harmonic oscillator state are not essential to the question of which fraction of light scattering is coherent or incoherent. Our experiment demonstrates the potential of using atomic Mott insulators to create single-atom wave packets for fundamental studies.