Bright tripartite entanglement in triply concurrent parametric oscillation

We show that an optical parametric oscillator based on three concurrent χ⁽²⁾ nonlinearities can produce, above threshold, bright output beams of macroscopic intensities which exhibit strong tripartite continuous-variable entanglement. We also show that there are two ways that the system can exhibit a three-mode form of the Einstein-Podolsky-Rosen paradox, and calculate the extracavity fluctuation spectra that may be measured to verify our predictions.