Tunable Continuous-Variable Tripartite Entanglement via Cascaded Third-Order Nonlinear Processes in a Ring Cavity

In this study, a tunable continuous-variable (CV) triple-mode entanglement scheme generated by cascading a spontaneous parametric four-wave and a sum-frequency four-wave mixing process is proposed. The entanglement feature of the triple-mode is demonstrated by using a sufficient inseparability criterion. It is confirmed that the triple-mode CV entanglement property, including the degree of violation of the sufficient inseparability criterion and the entanglement range in the frequency domain, can be modulated dynamically by modifying the nonlinear susceptibility and optical parameters. In particular, the intensity of the pumping field affects the modulation of the degree of entanglement, and the splitting of the entanglement spectrum comes from electromagnetically induced transparency. Although changing the relative detuning between the Stokes and anti-Stokes fields can increase the entanglement degree of the triple-mode, it results in the expansion of the entanglement range in frequency as well. Furthermore, although nonlinear susceptibility directly improves the degree of triple-mode CV entanglement, optical detuning related nonlinear dispersion has an indirect effect as well. Such an optical triple-mode CV entanglement with tunable properties can find applications in all-optical quantum communication and pave the way for the generation and manipulation of multichannel quantum networks.