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Journal of Modern Optics

Anisotropic narrowing of biphoton wave packet distribution in spontaneous parametric down-conversion with biaxial crystal

Guangwen Huo, Tongyi Zhang, Meizhi Zhang, Haiyan Zhu, Xin-Wei Zha, Heng Chen

Published Oct 26, 2017• 1 citation
Publisher

Abstract

We investigate theoretically the strong anisotropy in the wave packet distribution of biphoton pairs generated via spontaneous parametric down-conversion (SPDC) process with biaxial crystals. From the angle relationship in biaxial crystals, we deduce the wave function of type I SPDC by considering the longitudinal detuning under paraxial approximation. Taking BiB3O6 (BIBO) as an example, we numerically simulate the single-particle and coincidence distributions in two observation planes under the optimum phase-matching scheme. In contrast to uniaxial crystals, a stronger anisotropy effect and a higher entanglement of the photon pair states are obtained, which are attributed to the complex structure of biaxial crystals. These results are important for the generation of highly entangled biphoton pairs, especially for multi-photon pairs generation.

DOI
10.1080/09500340.2017.1393568

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We investigate theoretically the strong anisotropy in the wave packet distribution of biphoton pairs generated via spontaneous parametric down-conversion (SPDC) process with biaxial crystals. From the angle relationship in biaxial crystals, we deduce the wave function of type I SPDC by considering the longitudinal detuning under paraxial approximation. Taking BiB3O6 (BIBO) as an example, we numerically simulate the single-particle and coincidence distributions in two observation planes under the optimum phase-matching scheme. In contrast to uniaxial crystals, a stronger anisotropy effect and a higher entanglement of the photon pair states are obtained, which are attributed to the complex structure of biaxial crystals. These results are important for the generation of highly entangled biphoton pairs, especially for multi-photon pairs generation.
Wave packet structure of biphoton states arising in the process of spontaneous parametric down-conversion (SPDC) is studied theoretically and experimentally, and its relation with entanglement is discussed. In theory, a new expression is found for the biphoton wave function, in which anisotropy of the crystal refractive index is properly taken into account. Under the conditions of the experiment we report, the anisotropy effects are shown to be very strong. A scheme, optimal for observing extremely narrow coincidence angular photon distributions is found to be that in which the plane containing both the laser axis and the optical axis of a crystal coincides with the observation plane. The opposite, commonly investigated, case is that when these two planes are orthogonal to each other. We show that in the optimal geometry the coincidence angular distribution can be almost 20 times narrower than in the traditional scheme of measurements, and about 10 times narrower than the pump. Narrowing of coincidence distributions in the optimal geometry is accompanied by broadening the single-particle distributions, and this broadening is stronger pronounced in the optimal than in the commonly used geometry. The ratio R of widths of the single-particle and coincidence distributions in the optimal geometry appears to be as large as about 100, and we interpret this as an appropriate evaluation of the degree of entanglement accumulated in biphoton states. The results described are obtained theoretically and perfectly confirmed experimentally.
We theoretically investigate the effective nonlinear coefficient d eff of spontaneous parametric down-conversion (SPDC) process in biaxial nonlinear crystal BiB3O6 (BIBO). We solve the Fresnel equations in the collinear degenerate down-converted configuration, and get the relations of phase-matching angles. Considering the double phase-matching, we compute the phase-matching angles with different wavelength. Furthermore, we simplify the expression of effective nonlinear coefficient out of the principal planes, and numerically calculate it varying with the angle and wavelength. These results indicate that there are three effective phase-matching schemes for SPDC which can be used to construct a system to generate entangled photon pairs.
We show that the wave packet of a biphoton generated via spontaneous parametric down-conversion is strongly anisotropic. Its anisotropic features manifest themselves very clearly in comparison with measurements performed in two different schemes: When the detector scanning plane is perpendicular or parallel to the plane containing the crystal optical axis and the laser axis. The first of these two schemes is traditional whereas the second one gives rise to such unexpected results, such as anomalously strong narrowing of the biphoton wave packet measured in the coincidence scheme and very high degree of entanglement. The results are predicted theoretically and confirmed experimentally.
In this paper, we report on the collinear spontaneous parametric down conversion (SPDC) with quantum theory in angle picture. Based on angle-dependent refractive index of biaxial crystal and the dielectric dispersion, we numerically simulate the effective nonlinear coefficients of BiB 3 O 6 (BIBO) crystal in principle planes. The results indicate that the most effective phase matching scheme is the type I in yz plane, while the secondary options are the type I, type II in xz plane. Considering the derivation of angular phase matching conditions, the calculation is convenient, and it is superior in determination of the spatial distribution of entangled photons.
We analyze and optimize the parameters of the Type I spontaneous parametric down-conversion (SPDC) process in BiB3O6 (BIBO) crystal directly from calculations. This can be used to construct a system to generate ultrafast entangled photon pairs, which play an important role in quantum communication, quantum positioning, and quantum clock synchronization. Our work on the problem makes it clear that the optimal phase matching orientation in the process of SPDC is a key mechanism in the BIBO crystal in a way that appears not to have been appreciated before. In the case of ω = 0.405 μm , the numerical results of the optimization parameters at room temperature ( 295 K ) are:θ = 152.00° ,φ = 90° , and d eff = 3.48 pm/V . Finally, we use a pair of 0.6 mm thick biaxial BIBO crystals to construct an ultrafast entangled photon source, where the crystals are stacked together perpendicularly and pumped by a 405 nm pulsed laser doubling from a Tsunami mode-locked Ti:sapphire laser.
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.