Four types of non-Gaussian squeezed states and their entanglement properties
Zhang Da, Yanwen Zhang, Juan Gao · Physical Review A · 2025
We investigate the coupling of the fully degenerate triple-photon state generated by three-mode spontaneous parametric down-conversion with the vacuum at a beam splitter via numerical modeling. By using fully degenerate triple-photon states with distinct pump phases as input states, four different squeezed states are extracted at the output, which can be referred to as zero-phase, $\ensuremath{\pi}/2$-phase, $\ensuremath{\pi}$-phase, and $3\ensuremath{\pi}/2$-phase positive Wigner squeezed states. The non-Gaussianity evolution during the coupling process is quantitatively analyzed via quantum relative entropy, and the entanglement between the two output modes is confirmed from an entropic perspective. Furthermore, the entanglement properties of the zero-phase and $\ensuremath{\pi}$-phase positive Wigner squeezed states at the third- and sixth-order moments are revealed by applying the partial transpose positive criterion based on the higher-order covariance matrix. In particular, it is found that the steerability of the two output modes at the third- and sixth-order moments can be dynamically controlled by adjusting the intensity of the input light and the transmission of the beam splitter. These results enrich the repertoire of squeezed states in quantum optics and offer a feasible approach for the deterministic preparation of non-Gaussian entanglement via coupling fully degenerate triple-photon states with vacuum.