  Spontaneous parametric down-conversion (SPDC) in a laser pumped optical
nonlinear medium can produce heralded single photons with a high purity but a
very low yield. Improving the yield by increasing the pump power in SPDC
inevitably reduces the purity due to excitation of multi-photon events. We
propose a scheme to overcome this purity-yield trade-off by suppressing
multi-photon events in a cavity-enhanced SPDC via the photon blockade effect.
By introducing a strong photon-photon interaction into the intracavity medium
and increasing the pump power, we can improve the available single-photon yield
to larger than $90\%$, while maintaining a high purity of $99\%$, towards
on-demand generation of single photons through the SPDC process. Our
quasi-on-demand SPDC sources may boost single-photon-based quantum information
technology.
