Non-Gaussian nature and entanglement of spontaneous parametric nondegenerate triple-photon generation
Da Zhang, Yin Cai, Zhan Zheng, David Barral, Yanpeng Zhang, Min Xiao, Kamel Bencheikh
Abstract
We theoretically demonstrate through numerical methods that the triple-photon state generated by three-photon spontaneous parametric down-conversion is a non-Gaussian Greenberger-Horne-Zeilinger state, showing super-Gaussian statistics. Interestingly, the degree of entanglement between the modes of the triple-photon state is stronger than that corresponding to the two-mode squeezed vacuum state produced by a quadratic Hamiltonian with the same parameters. Furthermore, we propose a model to prepare two-mode sub-Gaussian entangled states with a tunable negative Wigner function based on quadrature projection measurements. We find that these Gaussian projection measurements with outcomes $X\ensuremath{\ge}1$ not only improve the entanglement of the residual two modes but also introduce a Gaussian component, resulting in the coexistence of Gaussian and non-Gaussian entanglement.