Two-body Kapitza-Dirac scattering of one-dimensional ultracold atoms

Kapitza-Dirac scattering, the diffraction of matter waves from a standing light field, is widely utilized in ultracold gases, but its behavior in the strongly interacting regime is an open question. Here, we develop a numerically exact two-body description of Kapitza-Dirac scattering for two contact-interacting atoms in a one-dimensional harmonic trap subjected to a pulsed optical lattice, enabling us to obtain the numerically exact dynamics. We map how interaction strength, lattice depth, lattice wave number, and pulse duration reshape the diffraction pattern, leading to an interaction-dependent population redistribution in real and momentum space. By comparing the exact dynamics to an impulsive sudden-approximation description, we delineate the parameter regimes where it remains accurate and those, notably at strong attraction and small lattice wave number, where it fails. Our results provide a controlled few-body benchmark for interacting Kapitza-Dirac scattering and quantitative guidance for Kapitza-Dirac-based probes of ultracold atomic systems.