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

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