  Entangled photon pairs are crucial resources for quantum information
processing protocols. Via the process of spontaneous parametric down-conversion
(SPDC), we can generate these photon pairs using bulk nonlinear crystals.
Traditionally, the crystal is designed to satisfy specific type of
phase-matching condition. Here, we report controllable transitions among
different types of phase-matching in a single periodically poled potassium
titanyl phosphate (PPKTP) crystal. By carefully selecting pump conditions, we
can satisfy different phase-matching conditions. This allows us to observe
first-order type-II, fifth-order type-I, third-order type-0, and fifth-order
type-II SPDCs. The temperature-dependent spectra of our source were also
analyzed in detail. Finally, we discussed the possibility of observing more
than nine SPDCs in this crystal. Our work not only deepens the understanding of
the physics behind phase-matching conditions, but also offers the potential for
a highly versatile entangled biphoton source for quantum information research.
