Quantum limits for cascaded nondegenerate optical parametric oscillators

The continuous variable multicolor entangled state of optical modes is one of the essential quantum resources for constructing quantum information networks composed of many nodes and channels. It has been well proved that the cascaded nondegenerate optical parametric oscillators (CNOPOs) are the most successful devices to produce bright entangled optical beams with different wavelengths. Here, we discuss the dependence of the possibly obtained largest-size multicolor entangled state and the entanglement degree on optical parameters of CNOPOs. Each NOPO in the cascaded system is operated above its oscillation threshold. One of two output optical beams produced by a NOPO is used for the pump light of the subsequent one, and the remained another beam serves as a submode of the multicolor entangled state. The obtainable maximal number of entangled submodes and the multicolor entanglement degree are numerically calculated under experimentally accessible conditions. The calculated results provide direct references for the design of generation systems of multicolor entangled optical beams.