We have experimentally investigated laser diffraction on electromagnetically induced gratings in a degenerate open two-level system. The experiment employs the standard backward four-wave mixing configuration and the open 6S 1/2 (Fϭ4)→6 P 3/2 (FЈϭ4) transition of cold cesium atoms. Population and coherence gratings are accessed for different relative polarizations of the incident laser beams. Natural and subnatural linewidths are observed depending on which frequency of the incident beams is scanned and reveal the effect of the atomic motion on the diffraction spectra. A simple theoretical model using a three-level ⌳ system is in reasonable agreement with the observed results and allowed us to make a close connection with the phenomenon of electromagnetically induced transparency.

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Nearly degenerate four-wave mixing (NDFWM) within a closed degenerate two-level atomic transition is theoretically and experimentally examined. Using the model presented by A. Lezama et al [Phys. Rev. A 61, 013801 (2000)] the ND-FWM spectra corresponding to different pump and probe polarization cases are calculated and discussed. The calculated spectra are compared to the observation of NDFWM within the 6S 1/2 (F = 4) → 6P 3/2 (F = 5) transition of cesium in a phase conjugation experiment using magneto optically cooled atoms.

Optical-pumping-induced population-grating transfer between hyperfine levels of the cesium D 2 line is observed through four-wave mixing in a sample of cold atoms. Diffraction efficiencies of order of 1% have been measured for a large range of angular apertures. We have studied the angular dependence of the diffracted signal in the limit of small atomic velocities and discussed its application for a nondestructive diagnostic of the trap dynamic. Image processing with nearly degenerate frequency conversion was also demonstrated using this specific mechanism.

Susceptible-infected (SI) and susceptible-infected-susceptible (SIS) are simple agent-based models often employed in epidemic studies. Both models describe the time evolution of infectious diseases in networks whose vertices are either susceptible (S) or infected (I) agents. Precise estimation for disease spreading is one of the major goals in epidemic studies but often restricted to heavy numerical simulations. Analytic methods using operatorial content are subject to the asymmetric eigenvalue problem, limiting the use of perturbative methods. Numerical methods are limited to small populations, since the vector space increases exponentially with population size N. Here, we propose the use of the squared norm of the probability vector to obtain an algebraic equation, which permits the evaluation of stationary states in Markov processes. The equation requires the eigenvalues of symmetrized time generators and takes full advantage of symmetries, reducing the time evolution to an O(N) sparse problem. The calculation of eigenvalues employs quantum many-body techniques, while the standard perturbation theory accounts for small modifications to the network topology.