  Interference is central to quantum physics and occurs when indistinguishable
paths exist, like in a double-slit experiment. Replacing the two slits with two
single atoms introduces optical non-linearities for which nontrivial
interference phenomena are predicted. Their observation, however, has been
hampered by difficulties in preparing the required atomic distribution,
controlling the optical phases and detecting the faint light. Here we overcome
all of these experimental challenges by combining an optical lattice for atom
localisation, an imaging system with single-site resolution, and an optical
resonator for light steering. We observe resonator-induced saturation of
resonance fluorescence for constructive interference of the scattered light and
nonzero emission with huge photon bunching for destructive interference. The
latter is explained by atomic saturation and photon pair generation. Our
experimental setting is scalable and allows one to realize the Tavis-Cummings
model for any number of atoms and photons, explore fundamental aspects of
light-matter interaction, and implement new quantum information processing
protocols.
