SPDC pair state
= SPDC pair state
{c}
{title2=$|\Psi\rangle\simeq|0,0\rangle+\eta|1,1\rangle$}
The weak-gain state generated by an undepleted pump contains a vacuum term and a photon-pair amplitude. A continuum pair amplitude combines the pump spectrum with a phase-matching factor $L\operatorname{sinc}(\Delta kL/2)e^{i\Delta kL/2}$. Its joint spectrum determines spectral correlations and the purity attainable by heralding one partner.