  If identical photons meet at a semi-transparent mirror they appear to leave
in the same direction, an effect called "two-photon interference". It has been
known for some time that this effect should occur for photons generated by
dissimilar sources with no common history, provided the easurement cannot
distinguish between the photons. Here we report a technique to observe such
interference with isolated, unsynchronized sources whose coherence times differ
by several orders of magnitude. In an experiment we interfere photons generated
via different physical processes, with different photon statistics. One source
is stimulated emission from a tuneable laser, which has Poissonian statistics
and a nano-eV bandwidth. The other is spontaneous emission from a quantum dot
in a p-i-n diode with a micro-eV linewidth. We develop a theory to explain the
visibility of interference, which is primarily limited by the timing resolution
of our detectors.
