Criterion for Single Photon Sources

We propose a criterion to classify and compare sources of single photons: the $p$-norm of their $k$th-order photon correlations. While ideally one should use the uniform norm with $p\rightarrow\infty$, in practice, the 3-norm already allows a meaningful comparison and shows the serious limitations of the usual criterion based on the second order correlation $g^{(2)}$ only. We apply this new criterion to a large family of popular single photon sources and show that some of them do not, in fact, qualify for this function. The best sources from our selections consist of a cascade of two-level systems, improving on the otherwise standard low-power resonant excitation of a single two-level system.