State measurement by photon filtering in a ring cavity

We suggest a method for measuring the photon number distribution and the density matrix of a single-mode radiation field. The setup consists of a chain of active ring cavities, each fed by a strong coherent probe and coupled to the signal through cross-Kerr phase modulation. Each cavity is set at resonance by a different Fock component of the signal, so that the detection probability at the cavities output is proportional to the signal photon statistics. The off-diagonal elements of the density matrix can be evaluated by measuring the photon statistics of a set of displaced signal states. The suggested setup allows a reliable state measurement even with low quantum efficiency at detectors.