  We perform a comprehensive set of experiments that characterize bosonic
bunching of up to 3 photons in interferometers of up to 16 modes. Our
experiments verify two rules that govern bosonic bunching. The first rule,
obtained recently in [1,2], predicts the average behavior of the bunching
probability and is known as the bosonic birthday paradox. The second rule is
new, and establishes a n!-factor quantum enhancement for the probability that
all n bosons bunch in a single output mode, with respect to the case of
distinguishable bosons. Besides its fundamental importance in phenomena such as
Bose-Einstein condensation, bosonic bunching can be exploited in applications
such as linear optical quantum computing and quantum-enhanced metrology.
