Spontaneous parametric down-conversion

SPDC occurs when a pump photon interacts with a nonlinear crystal lacking inversion symmetry, such as beta-barium borate (BBO) or lithium niobate. The crystal's nonlinear susceptibility mediates the spontaneous decay of the pump photon into two lower-energy photons, subject to conservation of energy and momentum (phase matching). The process is quantum mechanical in nature: the vacuum fluctuations of the electromagnetic field seed the down-conversion, and the output photons are generated in pairs that are strongly correlated in time and frequency.

Phase matching can be achieved by angle tuning (critical) or temperature tuning (noncritical) of the crystal, and by using different polarization configurations (type I or type II). In type I, signal and idler have the same polarization; in type II, they are orthogonal. The efficiency of SPDC is typically very low, on the order of 10⁻⁶ to 10⁻⁸ per pump photon, but the process is still practical because of the high photon flux available from lasers.

The two photons produced by SPDC are entangled in various degrees of freedom, including polarization, momentum, and energy-time. Polarization entanglement is most commonly exploited: by using a type-II crystal, the signal and idler photons can be prepared in a Bell state, such as |H⟩|V⟩ + |V⟩|H⟩. This was first demonstrated by Kwiat et al. in 1995, who used a BBO crystal to produce high-fidelity polarization-entangled pairs.

Energy-time entanglement arises because the emission time of the pair is uncertain, leading to correlations in the arrival times of the photons. This has been used for quantum clock synchronization and for tests of Bell inequalities. The high degree of correlation also enables applications in quantum metrology, such as sub-shot-noise interferometry and quantum-enhanced imaging.

SPDC is the workhorse for generating entangled photons in quantum information science. It is used in quantum key distribution (QKD) protocols, such as the Ekert protocol, where the entanglement is used to guarantee security. It also underpins quantum teleportation, where the entangled pair serves as a resource for transferring quantum states between distant parties.

In addition, SPDC sources are used in quantum computing with photonic qubits, as demonstrated by the BosonSampling experiments. They are also employed in quantum imaging, such as ghost imaging and quantum illumination, where the correlations between the photons allow imaging with low light levels. Furthermore, SPDC is used to generate heralded single photons, which are essential for many quantum photonic technologies.

Beyond the standard continuous-wave operation, SPDC can be implemented in pulsed regimes, enabling the generation of time-bin entangled photons. This is particularly useful for fiber-based quantum communication. Also, the process can be engineered to produce high-dimensional entanglement, where the photons are entangled in more than two levels, increasing the information capacity per photon.

An often-overlooked aspect is the role of SPDC in fundamental tests of quantum mechanics, such as the violation of Bell inequalities. The first such experiments used atomic cascades, but SPDC sources have become the standard due to their high brightness and controllability. Moreover, SPDC is not limited to visible wavelengths; it can be used to generate photons in the mid-infrared and even terahertz ranges, which is useful for spectroscopy and sensing.

Another niche application is in the generation of squeezed light, where the down-converted photons are in a squeezed vacuum state. This is used in gravitational-wave detectors, such as LIGO, to reduce quantum noise. Finally, SPDC has been proposed for quantum repeaters, which are essential for long-distance quantum communication.

Signal and idler photons

The two lower-energy photons produced in SPDC; conventionally, the signal has higher frequency than the idler.

Phase matching

The condition that ensures momentum conservation in the nonlinear process, often achieved by angle or temperature tuning.

Type I and type II

Configurations of SPDC where the signal and idler have the same (type I) or orthogonal (type II) polarizations.

Bell state

A maximally entangled quantum state of two qubits, such as |Φ⁺⟩ = (|HH⟩ + |VV⟩)/√2.

Heralded single photon

A single photon whose presence is signaled by the detection of its twin photon.