  We approach the strong-coupling thermodynamic limit in the response of the
open driven Jaynes-Cummings (JC) oscillator. We do so by highlighting the role
of quantum fluctuations against the semiclassical response in three distinct
regimes of operation. We begin by demonstrating the persistence of photon
blockade, predicted in [H. J. Carmichael, Phys. Rev. X 5, 031028 (2015)], as a
manifestation of the inherently-quantum and nonlinear JC spectrum revealed for
vanishing dissipation. We then proceed to discuss the importance of
bistability, which, despite being present in photon blockade, is able to
provide an alignment between the semiclassical nonlinearity and quantum
dynamics only for a driving amplitude having the same order of magnitude as the
light-matter coupling strength. This resolution brings us to the critical point
of the well-known quantum phase transition of second order on resonance, where
the quantum and semiclassical pictures are once more contrasted for a varying
participation of the two coherent interactions when going through the collapse
of the quasi-energy spectrum.
