  Using Keldysh field theory, we find conditions for non-equilibrium
condensation in the open Tavis-Cummings model under a direct finite-bandwidth
incoherent cavity drive. Experimentally, we expect the condensation transition
to be easily accessible to hybrid superconducting systems coupled to
microscopic spins, as well as to many other incoherently driven light-matter
systems. In our theoretical analysis, we explicitly incorporate the drive's
spectral distribution into the saddle-point description. We show that the
injected incoherent photons create a drive-dependent effective coupling between
spin-1/2 particles. The condensation transition arises at a critical regime of
driving which we can now accurately predict. Our results also provide important
guidelines for future quantum simulation experiments of non-equilibrium phases
with hybrid devices.
