  We report direct observations of photon-mediated spin-exchange interactions
in an atomic ensemble. Interactions extending over a distance of 500 microns
are generated within a cloud of cold rubidium atoms coupled to a single mode of
light in an optical resonator. We characterize the system via quench dynamics
and imaging of the local magnetization, verifying the coherence of the
interactions and demonstrating optical control of their strength and sign.
Furthermore, by initializing the spin-1 system in the mF = 0 Zeeman state, we
observe correlated pair creation in the mF = +/- 1 states, a process analogous
to spontaneous parametric down-conversion and to spin mixing in Bose-Einstein
condensates. Our work opens new opportunities in quantum simulation with
long-range interactions and in entanglement-enhanced metrology.
