  Cavity-embedded quantum emitters show strong modifications of free space
radiation properties such as an enhanced decay known as the Purcell effect. The
central parameter is the cooperativity $C$, the ratio of the square of the
coherent cavity coupling strength over the product of cavity and emitter decay
rates. For a single emitter, $C$ is independent of the transition dipole moment
and dictated by geometric cavity properties such as finesse and mode waist. In
a recent work [Phys. Rev. Lett. 119, 093601 (2017)] we have shown that
collective excitations in ensembles of dipole-dipole coupled quantum emitters
show a disentanglement between the coherent coupling to the cavity mode and
spontaneous free space decay. This leads to a strong enhancement of the cavity
cooperativity around certain collective subradiant antiresonances. Here, we
present a quantum Langevin equations approach aimed at providing results beyond
the classical coupled dipoles model. We show that the subradiantly enhanced
cooperativity imprints its effects onto the cavity output field quantum
correlations while also strongly increasing the cavity-emitter system's
collective Kerr nonlinear effect.
