  We investigate a possibility to generate non-classical states in light-matter
coupled noisy quantum systems, namely the anisotropic Rabi and Dicke models. In
these hybrid quantum systems a competing influence of coherent internal
dynamics and environment induced dissipation drives the system into
non-equilibrium steady states (NESSs). Explicitly, for the anisotropic Rabi
model the steady state is given by an incoherent mixture of two states of
opposite parities, but as each parity state displays light-matter entanglement
we also find that the full state is entangled. Furthermore, as a natural
extension of the anisotropic Rabi model to an infinite spin subsystem, we next
explored the NESS of the anisotropic Dicke model. The NESS of this linearized
Dicke model is also an inseparable state of light and matter. With an aim to
enrich the dynamics beyond the sustainable entanglement found for the NESS of
these hybrid quantum systems, we also propose to combine an all-optical
feedback strategy for quantum state protection and for establishing quantum
control in these systems. Our present work further elucidates the relevance of
such hybrid open quantum systems for potential applications in quantum
architectures.
