  Photon correlations between the photoluminescence peaks of the Mollow triplet
have been known for a long time, and recently hailed as a resource for heralded
single-photon sources. Here, we provide the full picture of photon-correlations
at all orders (we deal explicitly with up to four photons) and with no
restriction to the peculiar frequency windows enclosing the peaks. We show that
a rich multi-photon physics lies between the peaks, due to transition involving
virtual photons, and thereby much more strongly correlated than those
transiting through the dressed states. Specifically, we show that such
emissions occur in bundles of photons rather than as successive, albeit
correlated, photons. We provide the recipe to frequency-filter the emission of
the Mollow triplet to turn it into a versatile and tunable photon source,
allowing in principle all scenarios of photon emission, with advantages already
at the one-photon level, i.e., providing more strongly correlated heralded
single-photon sources than those already known.
