  When two indistinguishable single photons are fed into the two input ports of
a beam splitter, the photons will coalesce and leave together from the same
output port. This is a quantum interference effect, which occurs because the
two possible paths where the photons leave in different output ports interfere
destructively. This effect was first observed in parametric downconversion by
Hong, Ou and Mandel, and then with single photons produced one after the other
by the same quantum emitter. With the recent development of quantum
information, a lot of attention has been devoted to this coalescence effect as
a resource for quantum data processing using linear optics techniques. To
ensure the scalability of schemes based on these ideas, it is crucial that
indistinguishable photons are emitted by a collection of synchronized, but
otherwise independent sources. In this paper, we demonstrate the quantum
interference of two single photons emitted by two independently trapped single
atoms, bridging the gap towards the simultaneous emission of many
indistinguishable single photons by different emitters. Our data analysis shows
that the coalescence observed is mostly limited by the wavefront matching of
the light emitted by the two atoms, and to a lesser extent by the motion of
each atom in its own trap.
