Condensation in hybrid superconducting-cavity-microscopic-spins systems with finite-bandwidth drive

Using Keldysh field theory, we find conditions for nonequilibrium 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 nonequilibrium phases with hybrid devices.