A short perspective on long crystals: broadband wave mixing and its application to ultrafast quantum optics

Conditional preparation of single photons using parametric downconversion: a recipe for purity

“…where the x-components are as defined in (13). Therefore, for set values of the pump angle and e-ray collection angle, from this relationship can be found the wavevector mismatch for each pair of frequencies of the daughter photons.…”

“…• will move the central collinear wavelength by over 10 nm [13]. For phasematching at a fixed central pump wavelength, the effect that the pump focusing has on the total joint spectrum (summed over all pump angles) is more pronounced for the e-ray than the o-ray due to the orientation of the phasematching function.…”

High-visibility nonclassical interference between intrinsically pure heralded single photons and photons from a weak coherent field

“…Recent advances in the preparation of a pure single-photon source help solve this problem. When a phase-matching condition is carefully engineered, a pure heralded single-photon state can be generated in SPDC crystals [10][11][12][13] and photonic crystal fibers [14][15][16][17].By using SPDC with the group velocity matching condition in a potassium-dihydrogen-phosphate (KDP) crystal [12], we prepared an intrinsically pure heralded singlephoton state, which interfered with a weak coherent state in a three-photon Hong-Ou-Mandel (HOM) interference [18] without spectral filtering. Our experiment is the first to demonstrate that spectrally pure heralded single photons can have high-visibility interference with weak coherent photons without any spectral filtering.The two-photon component of the final state of SPDC can be expressed aswhere f (ω s , ω i ) = φ(ω s , ω i )α(ω s + ω i ) is the joint spectral distribution function [19].…”

“…φ(ω s , ω i ) and α(ω s + ω i ) are the phase-matching function and the pump envelope function, and the subscripts s and i denote signal and idler photons, respectively. By carefully choosing the phase-matching condition, as described below, the joint spectral distribution function of the signal and idler photons can attain a factorable state [11], which satisfiesThe purity of the signal is defined as γ ≡ Tr(ρ 2 s ), wherê ρ s = Tr i (|ψ si ψ si |) is the reduced density operator of the signal. This purity is determined by the factorability of the joint spectral distribution f (ω s , ω i ) [12] and can be calculated numerically using Schmidt decomposition [10].…”

Focusing on factorability: space–time coupling in the generation of pure heralded single photons

“…Secondly, the wavevectors in the phasematching function given in Equation (4) are linked to the frequencies of the three fields through the dispersion relations of KDP. For e-ray propagation, the dispersion relationship is dependent on the angle subtended by the beam and the optic axis and it is for this reason that the phasematching function shifts with changes in the crystal angle relative to the direction of collinear travel [22]. Due to the nontrivial nature of the empirical Sellmeier equations for KDP, the relationship between the phasematched wavelengths and the crystal angle is not simple.…”