  Harnessing entanglement and quantum coherence plays a central role in
advancing quantum technologies. In quantum optical light-atom platforms, these
two fundamental resources are often associated with a Jaynes-Cummings model
description describing the coherent exchange of a photon between an optical
resonator mode and a two-level spin. In a generic nonlinear spin-boson system,
more photons and more modes will take part in the interactions. Here we
consider such a generalisation -- the two-mode multiphoton Jaynes-Cummings
(MPJC) model. We show how entanglement and quantum coherence can be optimally
generated and subsequently manipulated with it in experimentally accessible
parameter regimes. A detailed comparative analysis of this model reveals that
nonlinearities within the MPJC interactions produce genuinely non-Gaussian
entanglement, devoid of Gaussian contributions, from noisy resources. More
specifically, strong coherent sources may be replaced by weaker, incoherent
ones, significantly reducing the resource overhead, though at the expense of
reduced efficiency. At the same time, increasing the multiphoton order of the
MPJC interactions expedites the entanglement generation process, thus rendering
the whole generation scheme again more efficient and robust. We further explore
the use of additional dispersive spin-boson interactions and Kerr
nonlinearities in order to create spin coherence solely from incoherent sources
and to enhance the quantum correlations, respectively. As for the latter,
somewhat unexpectedly, there is not necessarily an increase in quantum
correlations due to the augmented nonlinearity. Towards possible applications
of the MPJC model, we demonstrate how to engineer arbitrary NOON states with
appropriately chosen experimental parameters.
