spdc

Spontaneous Parametric Down-Conversion (SPDC) is a nonlinear optical process in which a pump photon propagating through a nonlinear crystal is converted into two lower-energy photons, commonly referred to as the signal and idler. The process relies on the crystal’s second-order nonlinear susceptibility and requires phase matching to conserve momentum in addition to energy conservation, so that the pump frequency equals the sum of the two output frequencies.

In SPDC, the energy conservation relation is ω_p = ω_s + ω_i, and the momentum conservation (phase matching) condition is k_p = k_s + k_i (with adjustments for quasi-phase matching in periodically poled materials). SPDC can be configured in degenerate or nondegenerate arrangements, and in collinear or noncollinear geometries. Two main phase-matching schemes are used: type-I, where the signal and idler share the same polarization, and type-II, where the two photons have orthogonal polarizations. The brightness and spectral properties depend on crystal length, pump bandwidth, and the phase-matching conditions.

Common materials for SPDC include beta barium borate (BBO), lithium niobate (LiNbO3), and periodically poled potassium titanyl phosphate (PPKTP). SPDC can be implemented in bulk crystals or integrated into waveguides, with quasi-phase matching enabling broader or tailored wavelength selection and improved efficiency.

Applications of SPDC center on quantum information science. The photon pairs produced are often entangled in polarization, momentum, or time-energy, making SPDC a foundational source for quantum communication, quantum cryptography, Bell-test experiments, quantum teleportation, and heralded single-photon sources. Experimental setups typically employ filtering and coincidence counting to identify correlated photon pairs and manage spectral and spatial correlations to improve photon purity. Limitations include inherently low conversion efficiency and the sensitivity of phase matching to temperature and alignment.