The biaxial nonlinear crystal BiB₃O₆ as a polarization entangled photon source using non-collinear type-II parametric down-conversion

Group velocity of light in biaxial crystals

Based on the wave vector surface, we have derived the analytical expressions for the group velocity of light traveling in an optically biaxial crystal in an arbitrary direction. Our formulas are in terms of either the wave vector direction or the ray direction. An axis dispersion vector is introduced to specify the rotation of the dielectric frame in monoclinic and triclinic crystals, which is found to be responsible for the asymmetry of the group velocity surfaces of these two crystal systems when compared to their phase and ray velocity surfaces. Our formulas confirm that the group velocity of light in a nondissipative medium equals the ratio between the Poynting vector and the total energy density of the electromagnetic field. The group index of light is found to be decomposable into three parts: the ray index, the group index due to principal refractive index dispersion, and that due to axis dispersion. Numerical calculations are performed for the group velocity of light in ${\rm Sn}_2{\rm P}_2{\rm S}_6$ crystal at 550 nm wavelength. Our results show that the dispersion of the principal refractive indices has a considerable contribution to the group index.

Entangled photon-pair sources based on three-wave mixing in bulk crystals

Entangled photon pairs are a critical resource in quantum communication protocols ranging from quantum key distribution to teleportation. The current workhorse technique for producing photon pairs is via spontaneous parametric down conversion (SPDC) in bulk nonlinear crystals. The increased prominence of quantum networks has led to a growing interest in deployable high performance entangled photon-pair sources. This manuscript provides a review of the state-of-the-art bulk-optics-based SPDC sources with continuous wave pump and discusses some of the main considerations when building for deployment.

Asymmetry of the group velocity of light in monoclinic crystals

We have proved that compared to phase velocity and ray velocity surfaces, the group velocity surface of a monoclinic crystal has a reduced symmetry, due to the loss of the two mirror planes that contain the crystallographic b axis. We have derived a formula for calculation of the group velocity of the extraordinary light traveling in a principal plane of a biaxial crystal, which takes into account the rotation of the dielectric frame due to frequency dispersion. The maximum asymmetry of the group velocity of light traveling in the a-c plane is found to be 2.4% at 365 nm in BiB₃O₆ and 1.4% at 550 nm in Sn₂P₂S₆.

Numerical Investigation of High-Purity Polarization-Entangled Photon-Pair Generation in Non-Poled KTP Isomorphs

We investigated the high-purity entangled photon-pair generation in five kinds of “non-poled” potassium titanyl phosphate (KTP) isomorphs (i.e., KTiOPO4, RbTiOPO4, KTiOAsO4, RbTiOAsO4, and CsTiOAsO4). The technique is based on the spontaneous parametric down-conversion (SPDC) under Type II extended phase matching (EPM), where the phase matching and the group velocity matching are simultaneously achieved between the interacting photons in non-poled crystals rather than periodically poled (PP) KTPs that are widely used for quantum experiments. We discussed both theoretically and numerically all aspects required to generate photon pairs in non-poled KTP isomorphs, in terms of the range of the beam propagation direction (or the spectral range of photons) and the corresponding effective nonlinearities and beam walk-offs. We showed that the SPDC efficiency can be increased in non-poled KTP isomorphs by 29% to 77% compared to PPKTP cases. The joint spectral analyses showed that photon pairs can be generated with high purities of 0.995–0.997 with proper pump filtering. In contrast to the PPKTP case, where the EPM is achieved only at one specific wavelength, the spectral position of photon pairs in the non-poled KTP isomorphs can be chosen over the wide range of 1883.8–2068.1 nm.

Numerical Investigation of High-Purity Entangled Photon-Pair Generation in Ba3Mg3(BO3)3F3 Crystals

We investigate the high-purity entangled photon pair generation in a recently developed borate crystal, Ba3Mg3(BO3)3F3. The technique is based on the spontaneous parametric down-conversion under the extended phase matching (EPM), where the phase matching and the group velocity matching between the interacting photons are satisfied simultaneously in bulk crystals with point symmetry of orthorhombic mm2 (thus showing biaxial birefringence). We will discuss all the theoretical aspects required for the generation of photon pairs in mm2 biaxial crystals, which are much more complex than the cases of uniaxial crystals (e.g., β-BaB2O4 and LiNbO3) and periodically poled crystals that are widely used in the field. Our study includes theoretical and numerical investigations of two types of EPM and their corresponding effective nonlinearities and spatial walk-offs. The results show that two types of EPM are satisfied over the specific range in the direction of pump wave vector, corresponding to its spectral ranges of 876.15–1052.77 nm for Type I and 883.92–914.33 nm for Type II. The joint spectral analyses show that photon-pairs can be generated with high purities of 0.997 with a proper pump filtering (for Type II), and 0.833 even without pump filtering (for Type I).

Resource efficient source of multiphoton polarization entanglement

Current photon entangling schemes require resources that grow with the photon number. We present a new approach that generates quantum entanglement between many photons, using only a single source of entangled photon pairs. The different spatial modes, one for each photon as required by other schemes, are replaced by different time slots of only two spatial modes. States of any number of photons are generated with the same setup, solving the scalability problem caused by the previous need for extra resources. Consequently, entangled photon states of larger numbers than before are practically realizable.