Tripartite entanglement and threshold properties of coupled intracavity down-conversion and sum-frequency generation

The process of cascaded down-conversion and sum-frequency generation inside an optical cavity has been predicted to be a potential source of three-mode continuous-variable entanglement. When the cavity is pumped by two fields, the threshold properties have been analyzed, showing that these are more complicated than in well-known processes such as optical parametric oscillation. When there is only a single pumping field, the entanglement properties have been calculated using a linearized fluctuation analysis, but without any consideration of the threshold properties or critical operating points of the system. In this work we extend this analysis to demonstrate that the singly pumped system demonstrates a rich range of threshold behavior when quantization of the pump field is taken into account and that asymmetric polychromatic entanglement is available over a wide range of operational parameters.