Master equations for two qubits coupled via a nonlinear mode

A microscopic master equation describing the dynamics of two qubits coupled via a nonlinear mediator is constructed supposing that the two qubits, as well as the nonlinear mode, interact, each with its own independent bosonic bath. Generally speaking the master equation derived in this way represents a more appropriate tool for studying the dynamics of open quantum systems. Indeed we showthat it is more complex than the phenomenological master equation, constructed simply adding ad hoc dissipative terms.