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The process of cascaded downconversion and sum-frequency generation inside anoptical cavity has been predicted to be a potential source of three-modecontinuous-variable entanglement. When the cavity is pumped by two fields, thethreshold properties have been analysed, showing that these are morecomplicated than in well-known processes such as optical parametricoscillation. When there is only a single pumping field, the entanglementproperties have been calculated using a linearised fluctuation analysis, butwithout any consideration of the threshold properties or critical operatingpoints of the system. In this work we extend this analysis to demonstrate thatthe singly pumped system demonstrates a rich range of threshold behaviour whenquantisation of the pump field is taken into account and that asymmetricpolychromatic entanglement is available over a wide range of operationalparameters.

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