Quantum Zeno Effect in Detection of Itinerant Microwave Photons

We analyze detection of itinerant photons using a QND measurement. We show that the backaction due to the continuous measurement poses a fundamental limit for the fidelity of detection in such a scheme. We illustrate this using a setup where signal photons have to enter a cavity in order to be detected dispersively. The measurement signal in this approach is the phase shift imparted to an intense beam passing through a second cavity mode. The restrictions on the fidelity are a consequence of the Quantum Zeno effect, and we discuss both analytical results and quantum trajectory simulations of the measurement process. Finally, we briefly mention a possible experimental realisation in the context of superconducting circuit QED.