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Manipulation of qudits in optical tables is a difficult and nonscalable task. The use of integrated optical circuits opens new possibilities for the generation, manipulation, and characterization of high dimensional states besides the ease of transmission of these states through an optical fiber. In this work we propose photonic circuits to perform minimum quantum state tomography of path qudits and show how to determine all the constituents parameters of these circuits (beam splitters and phase shifters). Our strategies were based on the symmetries of the involved POVMs (positive operator-valued measures) suggested for minimum tomography and allowed us to obtain interferometers smaller than those obtained by other already known methods. The calculations of the transmittances and reflectivities of the beam splitters were made using the definition of probability operators in extended Hilbert spaces and the application of Naimark's theorem. The employment of equidistant states for the definition of the POVM elements allowed us to develop a recipe applicable to the tomography of qudits of any dimension, generalizing our scheme., Comment: 7+\epsilon pages, 4 figures, comments are welcome

A simplified theory for the wavepackets of the photons emitted during the read process of a quantum memory formed by cold atoms is provided. We arrive at analytical expressions for the single- and double-photon emissions, evidencing superradiant features in both cases. In the two-photon case, both photons are emitted in the same spatiotemporal mode, characterizing a superradiant emission of a Fock state of light with two excitations. Experiments confirm the theoretical predictions with a satisfactory agreement., Comment: 12 pages, 7 figures

Superradiance in an ensemble of atoms leads to the collective enhancement of radiation in a particular mode shared by the atoms in their spontaneous decay from an excited state. The quantum aspects of this phenomenon are highlighted when such collective enhancement is observed in the emission of a single quantum of light. Here we report a further step in exploring experimentally the nonclassical features of superradiance by implementing the process not only with single excitations, but also in a two-excitations state. Particularly we measure and theoretically model the wave-packets corresponding to superradiance in both the single-photon and two-photons regimes. Such progress opens the way to the study and future control of the interaction of nonclassical light modes with collective quantum memories at higher photon numbers., Comment: 5 pages, 4 figures. V2: substantial changes on the introductory part of the paper