  Spontaneous Parametric Down-Conversion (SPDC), also known as parametric
fluorescence, parametric noise, parametric scattering and all various
combinations of the abbreviation SPDC, is a non-linear optical process where a
photon spontaneously splits into two other photons of lower energies. One would
think that this article is about particle physics and yet it is not, as this
process can occur fairly easily on a day to day basis in an optics laboratory.
Nowadays, SPDC is at the heart of many quantum optics experiments for
applications in quantum cryptography, quantum simulation, quantum metrology but
also for testing fundamentals laws of physics in quantum mechanics. In this
article, we will focus on the physics of this process and highlight few
important properties of SPDC. There will be two parts: a first theoretical one
showing the particular quantum nature of SPDC and the second part, more
experimental and in particular focusing on applications of parametric
down-conversion. This is clearly a non-exhaustive article about parametric
down-conversion as there is a tremendous literature on the subject, but it
gives the necessary first elements needed for a novice student or researcher to
work on SPDC sources of light.
