: Single-photon sources and detectors

A photon is defined as an elementary excitation of a single mode of the quantized electromagnetic field.1 The concept of quantized electromagnetic radiation2 was first introduced by Planck in 1900 to explain the black-body radiation spectrum.3–5 It was also used by Einstein in 1905 to explain the photoelectric effect5–7 and by Compton in 1923 to explain the wavelength shift of scattered x-rays.8 The term “photon” was first introduced by G. N. Lewis in 1926.9 The formal quantization of the electromagnetic field was first performed by Dirac in 1927.10, 11 The mode k of the quantized electromagnetic field is labeled by its frequency νk , and a single photon in mode k has energy equal to hνk , where h is Planck’s constant. While the monochromatic definition of a photon implies delocalization in time, in practice one often talks about propagating “singlephoton states” that are localized to some degree in time and space. Mathematically, one can describe such states as superpositions of monochromatic photon modes.1 Much discussion can be found in the literature about the definition of a “photon wavefunction.”12 For the purposes of this review, we adopt the following operational definition of a single-photon state: given a detector that can determine the number of incident photons (in some finite-width frequency range) with 100% accuracy, a single-photon state is an excitation of the electromagnetic field (localized to some degree in both space and time) such that the detector measures exactly one photon for each incident state. Put another way, a single-photon state is one for which the photon-number statistics have a mean value of one photon and a variance of zero. In addition, since the results of quantum measurements may depend on the measurement procedure and apparatus, the physics of the measurement process itself must also be considered.13 Single-photon detectors typically work by sensing an electrical signal that results from the absorption of a photon.