Influence of pump brightness, self-Kerr and cross-Kerr effects on the entanglement of partially degenerate triple-photon state

Abstract

Abstract Recently, partially degenerate triple-photon states (TPS) generated by the third-order spontaneous parametric down-conversion have been observed in a superconducting cavity (2020, Phys. Rev. X 10, 011011). Their non-Gaussian entanglement properties, characterized by a series of high-order covariance matrices, have also been theoretically revealed. Here, we use the non-Gaussian entanglement criterion proposed in (2021, Phy. Rev. Lett. 127, 150502) and the logarithmic negativity to study the effect of pump brightness, self-Kerr and cross-Kerr interactions on the entanglement of partially degenerate TPS (PDTPS). We find that the brighter the pump, the easier the entanglement of PDTPS leap to higher-order covariance matrices. Although both self-Kerr and cross-Kerr interactions induce nonlinear phase shifts and weaken the entanglement of PDTPS, cross-Kerr interactions can effectively raise the threshold of entanglement loaded on the third-order covariance matrix. These results can contribute to our understanding of the mechanism of the generation of unconditional non-Gaussian entanglement.