  One of the paradigms of a small quantum system in a dissipative environment
is the decay of an excited atom undergoing spontaneous photon emission into the
fluctuating quantum electrodynamic vacuum. Recent experiments have demonstrated
that the gapped photon dispersion in periodic structures can give rise to novel
spontaneous-decay behavior including the formation of dissipative bound states.
So far, these effects have been restricted to the optical domain. Here, we
experimentally demonstrate similar behavior in a system of artificial atoms in
an optical lattice that decay by emitting matter-wave, rather than optical,
radiation into free space. By controlling the vacuum coupling and excitation
energy, we directly observe exponential and partly reversible, non-Markovian
dynamics and detect a tunable bound state containing evanescent matter waves
for emission at negative excitation energies. Our system provides a flexible
platform for the emulation of open-system quantum electrodynamics and studies
of dissipative many-body physics with ultracold atoms.
