  The realization of a high-efficiency microwave single photon detector is a
long-standing problem in the field of microwave quantum optics. Here we propose
a quantum non-demolition, high-efficiency photon detector that can readily be
implemented in present state-of-the-art circuit quantum electrodynamics. This
scheme works in a continuous fashion, gaining information about the arrival
time of the photon as well as about its presence. The key insight that allows
to circumvent the usual limitations imposed by measurement back-action is the
use of long-lived dark states in a small ensemble of inhomogeneous artificial
atoms to increase the interaction time between the photon and the measurement
device. Using realistic system parameters, we show that large detection
fidelities are possible.
