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The development of an efficient single microwave photon detector represents the open challenge of circuit QED and typically relies on the time-variation of the control field. Searching for the simple ready-to-go setup, we propose a microwave frequency single photon transistor device which can operate under continuous wave probing. It can be realized using an impedance-matched system of a three level artificial atom coupled to two microwave cavities both connected to input/output waveguides. Using an additional classical drive for the upper transition, we find the parameter space where a single photon control pulse can be fully absorbed by hybridized excited states. This subsequently leads to series of quantum jumps in the upper manifold and appearance of a photon flux leaving the second cavity through a separate input/output port. The resulting device is robust to dephasing processes and possesses low dark count rate.
