Compared with earlier investigations we follow a way of arising singularities in quasidistributions as related to nonclassical photocount and wave statistics for nonlinear optical processes described by Gaussian statistics, also from the point of view of testing functions. Further we illustrate a process of regularization of singular quasidistributions so that regularized quasidistributions can provide measurable quantities. Results obtained can be applied to optical down-conversion as well as to Raman scattering provided that classical strong coherent pumping fields are used.
The random Wigner distribution of Gaussian stochastic processes with covariance in S0(R2d)
Abstract We consider nonclassical wave and number quantum statistics, and perform a decomposition of quasidistributions for nonlinear optical down-conversion processes using Bessel functions. We show that negative values of the quasidistribution do not directly represent probabilities; however, they directly influence measurable number statistics. Negative terms in the decomposition related to the nonclassical behavior with negative amplitudes of probability can be interpreted as positive amplitudes of probability in the negative orthogonal Bessel basis, whereas positive amplitudes of probability in the positive basis describe classical cases. However, probabilities are positive in all cases, including negative values of quasidistributions. Negative and positive contributions of decompositions to quasidistributions are estimated. The approach can be adapted to quantum coherence functions.
Two twin beams with a shared signal beam and separated idler beams are used together with the photon-number-resolving postselection in the signal beam to arrive at two coupled beams with anticorrelations in photon-number fluctuations. Moreover, the beams exhibit the sub-Poissonian photon-number statistics in their marginal distributions under suitable conditions. The postselected fields with the increasing mean photon numbers are reconstructed from the experimental photocount histograms by the maximum likelihood approach. Also a suitable Gaussian fit of both original twin beams and simulation of the postselection process are applied to arrive at the corresponding photon-number distributions. Their nonclassical properties are analyzed by suitable nonclassicality criteria and quantified by the corresponding nonclassicality depths. Determining the appropriate quasidistributions of integrated intensities with negative values, the performance of different non-classicality criteria is judged. Properties of the postselected fields reached both by the used and ideal photon-number-resolved detectors are mutually compared.