| spontaneous parametric down-conversion | |
|---|---|
| Name | Spontaneous parametric down-conversion |
| Phenomenon | Nonlinear optical process |
| Fields | Quantum optics; Quantum information |
| Firstreported | 1970s |
| Related | Parametric oscillation, Nonlinear optics, Entanglement (quantum mechanics) |
spontaneous parametric down-conversion
Spontaneous parametric down-conversion (SPDC) is a nonlinear optical process in which a single high-energy photon is converted into a pair of lower-energy photons inside a nonlinear optical crystal under conservation of energy and momentum. It is a widely used source of correlated and entangled photon pairs and underpins many experiments in quantum optics, quantum information, and tests of fundamental quantum mechanics.
SPDC occurs when a pump photon at angular frequency ω_p traverses a medium with a second-order nonlinear susceptibility (χ^(2)) and spontaneously splits into two photons conventionally named signal (ω_s) and idler (ω_i) such that ω_p = ω_s + ω_i. The process is governed by energy conservation and phase matching (momentum conservation), and is a quantum-mechanically allowed spontaneous process driven by vacuum fluctuations. Early theoretical descriptions trace to nonlinear optics developed in the mid-20th century; experimental demonstrations and systematic use in quantum experiments expanded in the 1970s and 1980s. SPDC is important for producing heralded single photons, entangled pairs for Bell tests, and as a tool in quantum metrology.
Efficient SPDC requires phase matching to satisfy k_p = k_s + k_i inside the nonlinear medium. Phase matching techniques include birefringent phase matching in uniaxial and biaxial crystals and quasi-phase matching via periodic poling. Common nonlinear crystals used are beta barium borate (BBO), lithium niobate (LiNbO3), potassium titanyl phosphate (KTP), and periodically poled lithium niobate (PPLN). Temperature tuning, angular tuning, and engineered poling periods provide control over wavelength, bandwidth, and polarization of the emitted photons. Waveguide implementations in lithium niobate and silicon photonics platforms increase interaction length and brightness.
SPDC generates a quantum state that, in the low-gain regime, is approximated by a two-photon component atop the vacuum: |ψ⟩ ≈ |0⟩ + ε |1_s,1_i⟩ + O(ε^2), where ε is proportional to pump amplitude and nonlinearity. Correlations appear in frequency, momentum (direction), polarization, and time. Type-I and Type-II refer to polarization relationships between signal and idler; Type-II phase matching yields orthogonally polarized photons used in polarization-entanglement schemes. Energy-time entanglement and momentum entanglement are exploited in quantum key distribution and tests of nonlocality such as experiments inspired by Bell's theorem and performed by groups at institutions like University of Innsbruck, Institute for Quantum Optics and Quantum Information, and Oak Ridge National Laboratory.
A typical SPDC setup includes a continuous-wave or pulsed laser pump, spatial filtering and focusing optics, the nonlinear crystal with phase matching control, and collection optics leading to single-photon detectors such as avalanche photodiodes or superconducting nanowire detectors. Heralding uses detection of one photon (herald) to signal the presence of its partner. Implementations vary: bulk-crystal configurations (BBO) for free-space experiments; periodically poled waveguides (PPLN/PPLT) for integrated sources; and microresonators for cavity-enhanced SPDC. Laboratories at California Institute of Technology, University of Vienna, and industry groups at ID Quantique and QuantumCTek have deployed engineered SPDC sources for applied devices.
SPDC is foundational to experiments in quantum communication, quantum cryptography (e.g., entanglement-based quantum key distribution), quantum teleportation, quantum metrology, and quantum imaging (ghost imaging). Heralded single-photon sources based on SPDC feed linear optical quantum computing prototypes such as the Knill–Laflamme–Milburn (KLM) scheme. Entangled photons generated by SPDC enabled loophole-free Bell tests and underpin quantum networks and entanglement distribution experiments in field trials by organizations like European Space Agency collaborators and national research centers.
The theoretical description uses perturbative quantum electrodynamics in nonlinear media. The interaction Hamiltonian H_int ∝ ∫ χ^(2) E_p^{(+)} E_s^{(-)} E_i^{(-)} d^3r couples pump, signal, and idler modes; first-order perturbation yields the two-photon amplitude or joint spectral amplitude (JSA). The JSA encodes spectral and temporal correlations; Schmidt decomposition quantifies entanglement and purity. Phase-matching functions multiply the pump envelope to give overall correlations; group-velocity dispersion and higher-order dispersion terms affect bandwidth and temporal shape. Models extend to multimode SPDC, high-gain parametric fluorescence, and cavity-enhanced or waveguided architectures.
SPDC is intrinsically probabilistic and typically low-efficiency per pump photon; conversion efficiency depends on pump power, crystal length, nonlinearity, and mode overlap. Increasing brightness raises multi-pair emission probability, degrading heralded single-photon purity and entanglement visibility. Noise sources include detector dark counts, Raman scattering in fibers, fluorescence and pump leakage, and background photons. Strategies to improve performance include narrowband filtering, cavity enhancement, engineered phase matching to produce factorable JSAs, and use of superconducting detectors to reduce dark counts. Practical deployment balances brightness, purity, and heralding efficiency for targeted quantum information tasks.
Category:Nonlinear optics Category:Quantum optics Category:Quantum information science