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Crystals

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

Donghwa Lee, Ilhwan Kim, Kwang Jo Lee

Published Dec 21, 2020• 0 citations
Publisher

Abstract

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).

DOI
10.3390/cryst10121164

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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).
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Recent advances of high-quality lithium niobate (LN) on insulator technology have revitalized the progress of novel chip-integrated LN-based photonic devices and accelerated application research. One of the promising technologies of interest is the generation of entangled photon pairs based on spontaneous parametric down-conversion (SPDC) in LNs. In this paper, we investigated, theoretically and numerically, Type II SPDC in two kinds of LNs—undoped and 5-mol% MgO doped LNs. In each case, both non-poled and periodically poled crystals were considered. The technique is based on the SPDC under Type II extended phase matching, where the phase matching and the group velocity matching are simultaneously achieved between interacting photons. The proposed approach has not yet been reported for LNs. We discussed all factors required to generate photon pairs in LNs, in terms of the beam propagation direction, the spectral position of photons, and the corresponding effective nonlinearities and walk-offs. We showed that the spectral positions of the generated photon pairs fall into the mid-infrared region with high potential for free-space quantum communication, spectroscopy, and high-sensitivity metrology. The joint spectral analyses showed that photon pairs can be generated with high purities of 0.995–0.999 with proper pump filtering.
The generation and detection of nonclassical light of about 2 μm has good potential in an emerging field of high-sensitivity metrology, especially gravitational wave detection, as well as free-space quantum communication. A pair of photons is generated through a spontaneous parametric down-conversion (SPDC) process in a nonlinear optic crystal, which can be properly entangled in a spatial region where two beams with each polarization overlap or in a Sagnac-loop interferometer configuration. We investigated theoretically and numerically Type II SPDC in a potassium niobate (KNbO3, KN) crystal, which is useful as a material platform for generating photon pairs of high spectral purity in the 2-μm range. The technique is based on the frequency degenerate SPDC under Type II extended phase matching (EPM). We described the EPM characteristics of KN and showed that it is practically feasible for a 1064-nm pumped SPDC under moderate temperature conditions. The effective nonlinear optic coefficient of KN is at least four-times larger than those of other crystals using the Type II EPM approach, which implies a significant improvement in SPDC efficiency. The joint spectral analysis showed that a pair of photons can be generated with a high purity of 0.995 through proper pump filtering.
Abstract Spontaneous parametric down-conversion (SPDC) is the most widely used process for generating photon pairs entangled in various degrees of freedom such as polarization, time-energy, position-transverse momentum, and angle-orbital angular momentum (OAM). In SPDC, a pump photon interacts with a non-linear optical crystal and splits into two entangled photons called the signal and the idler photons. The SPDC process has been studied extensively in the last few decades for various pump and crystal configurations, and the entangled photon pairs produced by SPDC have been used in numerous experimental studies on quantum entanglement and entanglement-based real-world quantum-information applications. In this tutorial article, we present a thorough study of phase matching in BBO crystals for spontaneous parametric down-conversion and thereby also investigate the generation of entangled photons in such crystals. First, we present a theoretical derivation of two-photon wavefunction produced by SPDC in the frequency and transverse momentum bases. We then discuss in detail the effects due to various crystal and pump parameters including the length of the crystal, the angle between the optic axis and the pump propagation direction, the pump incidence angle on the crystal surface, the refraction at the crystal surfaces, and the pump propagation direction inside the crystal. These effects are extremely relevant in experimental situations. We then present our numerical and experimental results in order to illustrate how various experimental parameters affect the phase matching and thus the generation of entangled photons. Finally, using the two-photon wavefunction in the transverse wave-vector basis, we show how to derive the two-photon wavefunction in the OAM basis and thereby calculate the two-photon angular Schmidt spectrum. We expect this article to be useful for researchers working in various capacities with entangled photons generated by SPDC in BBO crystals.
We describe the full characterization of the biaxial nonlinear crystal BiB₃O₆ (BiBO) as a polarization entangled photon source using non-collinear type-II parametric down-conversion. We consider the relevant parameters for crystal design, such as cutting angles, polarization of the photons, effective nonlinearity, spatial and temporal walk-offs, crystal thickness and the effect of the pump laser bandwidth. Experimental results showing entanglement generation with high rates and a comparison to the well investigated β-BaB₂O₄ (BBO) crystal are presented as well. Changing the down-conversion crystal of a polarization entangled photon source from BBO to BiBO enhances the generation rate as if the pump power was increased by 2.5 times. Such an improvement is currently required for the generation of multiphoton entangled states.
We present a highly efficient source for discrete frequency-entangled photon pairs based on spontaneous parametric down-conversion using 3rd-order type-0 quasi-phase matching in a periodically poled MgO-doped stoichiometric LiTaO(3) crystal pumped by a 355.66-nm laser. Correlated two-photon states were generated with automatic conservation of energy and momentum in two given spatial modes. These states have a wide spectral range, even under small variations in crystal temperature, which consequently results in higher discreteness. Frequency entanglement was confirmed by measuring two-photon quantum interference fringes without any spectral filtering.