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

General rules for bosonic bunching in multimode interferometers