Multi-color continuous-variable entangled optical beams generated by NOPOs

We propose an alternative scalable way to generate multi-color entangled optical beams efficiently utilizing the tripartite entanglement existent between three fields—signal, idler, and pump—from a nondegenerate optical parametric oscillator (NOPO) operating above the threshold. The special case of two cascaded NOPOs is studied, as it is shown that the five beams with very different frequencies are generated by NOPOA (one of the retained signal and idler beams, and the reflected pump beam) and NOPOB (the output signal and idler beams, and the reflected pump beam). These beams are theoretically demonstrated to be continuous variable (CV) entangled with each other by applying the positivity of the partially transposed criterion for the inseparability of multipartite CV entanglement. The symplectic eigenvalues of the partial transposition covariance matrix of the obtained optical entangled state are numerically calculated in terms of experimentally reachable system parameters. The optimal operation conditions to achieve high five-color entanglement are presented. As the cavity parameters and the nonlinear crystals of the two NOPOs can be chosen freely, the frequencies of the submodes in the entangled state thus are adjustable to match the transition frequencies of atoms or low loss fiber-optic communication window. The calculated results provide direct references for future experiment to generate multi-color entangled optical beams efficiently by means of NOPOs operating above the threshold.