More than eighty years ago, H. Bethe pointed out the existence of bound
states of elementary spin waves in one-dimensional quantum magnets. To date,
identifying signatures of such magnon bound states has remained a subject of
intense theoretical research while their detection has proved challenging for
experiments. Ultracold atoms offer an ideal setting to reveal such bound states
by tracking the spin dynamics after a local quantum quench with single-spin and
single-site resolution. Here we report on the direct observation of two-magnon
bound states using in-situ correlation measurements in a one-dimensional
Heisenberg spin chain realized with ultracold bosonic atoms in an optical
lattice. We observe the quantum walk of free and bound magnon states through
time-resolved measurements of the two spin impurities. The increased effective
mass of the compound magnon state results in slower spin dynamics as compared
to single magnon excitations. In our measurements, we also determine the decay
time of bound magnons, which is most likely limited by scattering on thermal
fluctuations in the system. Our results open a new pathway for studying
fundamental properties of quantum magnets and, more generally, properties of
interacting impurities in quantum many-body systems.Comment: 8 pages, 7 figure
