QUROPE Quantum Information Processing and Communication in Europe

We present a method for reconstructing the average evolution of the photon number distribution of a field decaying in a high-Qcavity. It applies an iterative maximum likelihood state reconstruction algorithm to the diagonal elements of the field density operator. It is based on quantum non-demolition measurements carried out with atoms crossing the cavity one by one. A small set of successively detected atoms defines a positive operator valued measure (POVM). The reconstruction is performed by applying this POVM to a large ensemble of field realizations. An optimal POVM based on the detection of a minimal number of atoms is shown to be sufficient to ensure an unambiguous convergence of the reconstruction. The cavity crossing time of this minimal number of atoms must be much shorter than the lifetime of the largest photon number present in the field. We apply the method to monitor the evolution of number states prepared by quantum feedback in a recent experiment. The method could also be useful in circuit QED experiments.