Direct Production of Tripartite Pump-Signal-Idler Entanglement in the Above-Threshold Optical Parametric Oscillator

We calculate the quantum correlations existing among the three output fields (pump, signal, and idler) of a triply resonant nondegenerate optical parametric oscillator operating above threshold. By applying the standard criteria [P. van Loock and A. Furusawa, Phys. Rev. A 67, 052315 (2003)], we show that strong tripartite continuous-variable entanglement is present in this well-known and simple system. Furthermore, since the entanglement is generated directly from a nonlinear process, the three entangled fields can have very different frequencies, opening the way for multicolored quantum information networks.

Figure 1

Optimized sum of variances, $S_1^{\min }$, for Eq. (3): $\sigma =\mathrm{\text{pump}}$ power relative to threshold, $\omega =\mathrm{\text{analysis}}$ frequency, in units of $1/\tau$.

Figure 2

Optimized sum of variances, $S_2^{\min }=S_3^{\min }$, for Eqs. (4, 5): $\sigma =\mathrm{\text{pump}}$ power relative to threshold, $\omega =\mathrm{\text{analysis}}$ frequency, in units of $1/\tau$.

Figure 3

Difference between logarithmic negativities, $E_N^{\mathrm{diff}}$, for the full three modes and for only signal and idler modes. $\sigma =\mathrm{\text{pump}}$ power relative to threshold, $\omega =\mathrm{\text{analysis}}$ frequency, in units of $1/\tau$.