Effective quantum dynamics induced by a driven two-level-system bath

We derive a Born-Markov master equation describing the dissipation induced by a bath of lossy but coherently driven two-level systems (TLSs) coupled to a bosonic system via Jaynes-Cummings interaction. We analytically derive all the master-equation rates. We characterize these rates for the particular case of a single-mode system coupled to identical TLSs. We study the steady state of the system and its exotic properties stemming from the nonthermal stationary state of the driven TLS bath. These properties include dissipative amplification, bath-induced linear instability, and both coherent and dissipative squeezing. The master equation is valid for arbitrarily strong TLS driving and it can be generalized to include multilevel systems or other system-bath interaction terms, among others. Our work provides a tool to study and characterize TLS-induced decoherence, a key limiting factor in quantum technological devices based on, for instance, superconducting circuits, magnonic systems, or quantum acoustics.