  We propose a microwave frequency single photon transistor which can operate
under continuous wave probing, and represents an efficient single microwave
photon detector. It can be realized using an impedance matched system of a
three level artificial ladder-type atom coupled to two microwave cavities
connected to input/output waveguides. Using a classical drive on the upper
transition, we find parameter space where a single photon control pulse
incident on one of cavities can be fully absorbed into hybridized excited
states. This subsequently leads to series of quantum jumps in the upper
manifold and the appearance of a photon flux leaving the second cavity through
a separate input/output port. The proposal does not require time variation of
the probe signals, thus corresponding to a passive version of single photon
transistor. The resulting device is robust to qubit dephasing processes,
possesses low dark count rate for large anharmonicity, and can be readily
implemented using current technology.
