  The term $N$-photon bundles has been coined for a specific type of photon
emission, where light quanta are released from a cavity only in groups of $N$
particles. This emission leaves a characteristic number distribution of the
cavity photons that may be taken as one of their fingerprints. We study this
characteristic $N$-photon bundle statistics considering two solid-state cavity
quantum electrodynamics (cQED) systems. As one example, we consider a
semiconductor quantum-dot--microcavity system coupled to longitudinal acoustic
phonons. There, we find the environmental influence to be detrimental to the
bundle statistics. The other example is a superconducting qubit inside a
microwave resonator. In these systems, pure dephasing is not important and an
experimentally feasible parameter regime is found, where the bundle statistics
prevails.
