Single-photon source

A single-photon source emits light in which no two photons arrive together: ideally, each trigger pulse produces exactly one photon, into a known spatial and spectral mode. This is a statement about photon statistics, and the figure of merit is the second-order correlation at zero delay, $g^{(2)}(0)$, which is 1 for a laser, 2 for thermal light and 0 for an ideal single-photon source. The best semiconductor quantum-dot sources report $g^{(2)}(0)$ of order 0.01 or below; heralded sources based on photon pairs reach a few percent or less when operated at low pair probability. They supply qubits for photonic quantum computing and some forms of quantum key distribution.

Why an attenuated laser falls short

A laser pulse attenuated to a mean of $\mu$ photons still has Poisson statistics. For $\mu = 0.1$, the probability of exactly one photon is 0.0905, the probability of two or more is 0.0047, and about 4.9% of the non-empty pulses carry more than one photon. Lowering $\mu$ reduces this fraction only in proportion to $\mu$, at the cost of mostly empty pulses, and $g^{(2)}(0)$ stays at 1 however weak the pulse is made.

Measuring g⁽²⁾(0)

The standard measurement is the Hanbury Brown and Twiss arrangement: the source is split by a 50:50 beam splitter onto two single-photon detectors, typically a single-photon avalanche diode pair or superconducting nanowire detectors, and a time tagger histograms the delays between clicks, as in time-correlated single-photon counting. For a pulsed source the histogram shows a peak every repetition period; the area of the zero-delay peak divided by the mean area of the side peaks gives $g^{(2)}(0)$.

For small multiphoton probabilities the correlation relates to the photon-number probabilities $P_n$ as

$$g^{(2)}(0) \approx \frac{2P_2}{P_1^{2}},$$

which is why a value of 0.01 corresponds to a two-photon probability far below the single-photon probability. Dark counts and background light add accidental coincidences and raise the measured value; published figures are often background-corrected.

Types of sources

Heralded photon pairs. Spontaneous parametric down-conversion or four-wave mixing creates photons in pairs; detecting one photon (the herald) announces the presence of its partner. The pair number in a single mode follows thermal statistics, so the heralded $g^{(2)}(0)$ grows in proportion to $\mu$, the mean pair number per pulse: it lies between about $2\mu$ for a fully efficient herald detector and $4\mu$ for an inefficient one. With $\mu = 0.01$ the heralded value is 0.02–0.04, and at an 80 MHz repetition rate the source creates about $8 \times 10^5$ pairs per second before any collection or detection loss. Purity and rate trade directly against each other; spatial or temporal multiplexing of many heralded sources is the route around the trade.

Quantum dots. An InAs dot embedded in GaAs behaves as an artificial atom: once excited, it emits one photon as it relaxes, and cannot emit a second until it is excited again. Emission is typically in the 900–950 nm range, the radiative lifetime is of order 1 ns, and an optical microcavity or waveguide shortens it through the Purcell effect and directs the emission into a collectable mode. Resonant picosecond excitation gives the highest purity, and the dots operate at a few kelvin.

Color centers and molecules. Defects in solids such as the nitrogen-vacancy center in diamond (zero-phonon line at 637 nm) and the silicon-vacancy center (737 nm), defects in hexagonal boron nitride, and single dye molecules all emit one photon per excitation cycle, and several work at room temperature. Their drawback is spectral: a large share of NV emission falls in the broad phonon sideband rather than the zero-phonon line, which limits indistinguishability.

Brightness and indistinguishability

Two further figures of merit matter. Brightness is the probability that a trigger delivers a photon into the first lens or into a single-mode fiber, and it is quoted inconsistently: "source brightness" at the first lens, fiber-coupled efficiency, and end-to-end efficiency including detectors differ by large factors. Indistinguishability measures whether successive photons are identical in frequency, bandwidth, polarization and arrival time; it is measured by Hong–Ou–Mandel interference of two photons on a beam splitter, where identical photons always exit together. Photonic quantum computing needs values near unity; quantum-dot sources have reported values above 0.9 together with fiber-coupled efficiencies of tens of percent.

Common questions

What g⁽²⁾(0) counts as a single-photon source?

Any value below 0.5 shows that the light cannot come from two or more independent emitters, and this threshold is the usual proof of single-emitter behavior. Practical applications ask for much lower values, typically 0.05 or below.

Is a heralded source a true single-photon source?

It is a probabilistic one: the heralded photon has low multiphoton content, but its arrival time is random unless the source is multiplexed. Deterministic sources such as quantum dots emit on demand, in a fixed time window after each trigger, although the probability of delivering a photon per trigger is still well below one.

Can single-photon sources be integrated on chips?

Heralded sources based on four-wave mixing in silicon or silicon nitride waveguides are routine parts of quantum photonic integrated circuits; quantum dots are being integrated by heterogeneous bonding and transfer printing.

References: B. Lounis, M. Orrit, Rep. Prog. Phys. 68, 1129 (2005); M. D. Eisaman, J. Fan, A. Migdall, S. V. Polyakov, Rev. Sci. Instrum. 82, 071101 (2011); P. Senellart, G. Solomon, A. White, Nature Nanotechnology 12, 1026 (2017); I. Aharonovich, D. Englund, M. Toth, Nature Photonics 10, 631 (2016); C. K. Hong, Z. Y. Ou, L. Mandel, Phys. Rev. Lett. 59, 2044 (1987); Mandel & Wolf, Optical Coherence and Quantum Optics (1995).