Figure 5
From: Orthogonal quasi-phase-matched superlattice for generation of hyperentangled photons
Comparison of the spatial characteristics of biphotons emitted by three LiNbO3 structures—cascaded (top), double-nonlinearity (middle), and superlattice (bottom)— of 5-mm overall length, excited by a 532-nm, 133-fs pulsed pump focused to a 50-μm waist. The downconversion is nondegenerate with signal and idler photons centered at 810 nm and 1550 nm, and noncollinear with the respective central emission angles 0.5° and 0.96° in free space, respectively. Ultra-wide band spectral filters (70-nm full width at half maximum) are used. (a) The biphoton probability distribution P H(x 1, x 2) for the HH component at the crystal exit plane z = 0 shown here at points on the x axis as a function p H(x 1, x 2) = P H(x 1, 0, x 2, 0). (b) Same as (a) but for the VV component. (c) Projections of p H(x 1, x 2) and p V(x 1, x 2) along the diagonal and off-diagonal directions as functions of (x 1 + x 2) and (x 1 − x 2), normalized to their respective maximum values. For the cascaded crystals (first row), the high quadratic relative-phase function in (q 1x  − q 2x ) axis in Fig. 4 introduces a magnifying distortion to the joint spatial correlations along (x 1 − x 2) axis. The superlattice and double-nonlinearity crystal have nearly perfect spatial indistinguishability. (d) Spatial purity \({\rm{Tr}}[{({\rho }_{{\rm{\Delta }}\lambda }^{{\bf{q}}})}^{2}]\) as a function of the spectral filter bandwidth Δλ (full width at half maximum). At Δλ = 0, the purity is unity for both the DN and SL structures, since the distinguishing frequency information is absent. As Δλ increases, the spatial purity is reduced, indicating that the spectral degree of freedom plays an increasing distinguishing role, together with the polarization degree of freedom.
