What exactly is "quantum entanglement" ？

In science, it refers to two particles that affect each other, even if they are far apart, as if bound together. Therefore, in theory, quantum entanglement means that there is no clear boundary between two states of a particle, and they can appear at the same time. This phenomenon is called "quantum entanglement".

The preparation of entangled particle pairs is the prerequisite for the experimental verification of Bell's inequality.

Scientists completed 12 experiments from 1972 to 1982, among which, the results of 10 experiments were consistent with the prediction of quantum mechanics and violated Bell's inequality. An experiment completed by Nobel laureate A. Aspect in 1982 is called "conclusive evidence" against local realism [1]. However, due to the complexity and importance of the debate between local realism and quantum mechanics, and the fact that there are still many "loopholes" in the experimental test of Bell's inequality, physicists have never stopped experimenting with Bell's inequality test. Research is also constantly seeking new and more efficient methods for preparing entangled photon pairs. A large number of experiments have been completed so far, and the BBO nonlinear optical crystal has played an important role in the development and progress of subsequent entangled photon experiments, and has gradually become the main method for preparing entangled photons by virtue of its advantages.

Of the 12 experiments completed before 1982, 7 used atomic cascade radiation photon pairs, 4 used annihilation radiation photon pairs, and 1 used proton pairs. Due to the inherent defects of these source technologies, for example, the idea of random delay selection is difficult to realize in the atomic cascade emission photon source, the experimental structure is complex, the efficiency is low, the stability is poor, and it is not easy to analyze. Therefore, most of the experiments completed after 1988 used a technique called optical spontaneous parametric down-conversion (PDC) to generate entangled photon pairs. There are two ways for a photon to become a photon pair through spontaneous parametric downconversion, depending on whether the two photons of the downconverted photon pair have the same polarization or orthogonal polarizations, which is why they are often referred to in the literature as type I (type-I) parameter down-conversion and type II (type-II) parameter down-conversion. This photon source has significant advantages. First, it is simple in structure, easy to implement, and easy to detect; secondly, it can generate two very small correlated photon beams, which can be input into a large length of optical fiber or transmitted in free space, so the light source It is allowed to be far away from the measurement device, which has exceeded thousands of kilometers at present, making the verification experiment more direct and objective. Since then, the method of using nonlinear optical crystals, especially BBO crystals, to prepare high-brightness entangled photon pairs has gradually become the mainstream.

Application of BBO crystals in entangled photon experiments.

In 1988, the group of Shih and Alley[2] published the article "New Type of Einstein-Podolsky-Rosen-Bohm Experiment Using Pairs of Light Quanta Produced by Optical Parametric Down Conversion", which was the first to use parametric down conversion technology and nonlinear optical An experimental report of Bell's inequality test for entangled photon pairs produced by crystals. The crystal used in the experiment is a type I phase-matched KD*P crystal (as shown in Figure 1). The experimental data is d=0.34±0.03, which shows a violation of 3 standard deviations of Freedman's inequality.This experiment opened the era of nonlinear optical crystals to prepare entangled photons. At this time, the BBO crystal is only used as an input light frequency doubling crystal to participate in the experiment, and the KD*P crystal generates entangled photons.

   Figure 1. Schematic diagram of the experimental setup

In 1992, Brendel, Mohler and Martiessen[3] published the article "Experimental Test of Bell's Inequality for Energy and Time", which was one of the earliest experiments to directly use BBO crystals to prepare entangled photon pairs. In a particularly simple and easy-to-analyze structure (as shown in Figure 2), the Bell inequality of energy and time was tested and verified, and except for the experiment based on "phase and momentum" completed by Rarity and Tapster in 1990, all previous experiments were for Examination of spin or polarization variables. The final experimental results achieved a maximum visibility of up to 86%, and a violation of Bell's inequality for energy and time with 7 standard deviations.

   Figure 2. Schematic diagram of the experimental setup

In 1993, Kiess, Shih, Sergienko and Alley[4] published the article "Einstein-Podolsky-Rosen-Bohm Experiment Using of Light Quanta Produced by Type-Ⅱ Parametric Down Conversion", which used BBO crystals for the first time in the type-Ⅱ phase matching parameter The entangled photon pairs generated in the down-conversion to test Bell's inequality. The experimental data they gave was S=0.316±0.003, and they stated in the text that the experiment violated Freedman's inequality with 22 standard deviations.

In 1998, Weihs, Jennewien, Simon, Weinfurter, and Zeilinger [5] published the paper "Violation of Bell's Inequality under Strict Einstein Locality Conditions". According to the type II parametric down-conversion principle, BBO crystals are selected to generate polarization-entangled photon pairs (as shown in Figure 3). In this experiment, the distance between the analyzer and the detector is 400m. The time is about 100ns, which is significantly shorter than the time (1.3ms) required for light to travel this distance, which meets the requirements of Einstein's localization conditions; each detector's analysis direction of local linear polarization is determined by an electron- Determined by the Photon's voltage regulator; direction selection is based on a random number generator. The final data of the experiment is S=2.73±0.02, which violates the CHSH inequality by more than 30 standard deviations. The importance of this experiment is that it is considered to be the first experiment that tried to surpass the Aspect experiment in 1982 and indeed achieved great success, because it is the first time that it has strictly implemented Einstein's locality conditions, and has closed the localization sexual vulnerability.

Figure 3. Schematic diagram of the experimental setup (Electro-Optic Modulator components are BBO crystals)

In 2003, Aspelmeyer, Zeilinger and other 13 authors[6] published the article "Long-Distance Free-Space Distribution of Quantum Entanglement" in Science magazine. The experiment in this paper uses polarization-entangled photon pairs produced by type II parametric down-converting BBO crystals. Unlike previous experiments, this experiment was completed for the first time in a free space separated by 600 meters without the aid of optical fiber transmission. Based on this, in 2005, the team of Jian-wei Pan of the University of Science and Technology of China and other 13 people [7] realized the distribution of entangled photons in a 13-kilometer-long free space, which was the longest distance at that time. Experiments have shown that the desired entanglement persists even when two entangled photons have traveled through a noisy urban environment (atmospheric background). Both experimental experiments are tests of the CHSH inequality, demonstrating a violation of Bell's inequality

In 2022, our scientists also realized the high-dimensional Bell inequality test without detection loopholes for the first time. The research group of Li Chuanfeng and Liu Biheng, a team of academician Guo Guangcan of the University of Science and Technology of China, used BBO crystals to prepare entangled photons, and raised the overall detection efficiency of high-dimensional entangled photons to 71.7 %[8], thereby realizing the high-dimensional Bell inequality test without detection loopholes (as shown in Figure 4). This achievement lays an important foundation for the further realization of the high-dimensional Bell inequality test that simultaneously closes detection loopholes and non-locality loopholes and the device-independent high-dimensional quantum communication process.

   Figure 4. Schematic diagram of the high-dimensional Bell inequality experimental setup without detection loopholes

Summary and Outlook

Today, although quantum entanglement has been confirmed, scientists still forge ahead on the path forward for quantum mechanics. Throughout the development history of entangled photon experiments, many important quantum entanglement experiments have used CRYSMIT' BBO crystals, which played an important role in the process of preparing entangled photons, and also gave us the opportunity to participate in this major philosophical debate in physics.

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[3] J.Brendel,E.Mohler,W.Martienssen.Experimental Test of Bell’s Inequality for Energy and Time[J].Europhys.Lett.,1992,20(7):575-580.

[4] T.Kiess,Y.H.Shih,A.Sergienko,C.Alley.Einstein-Podolsky-Rosen-Bohm Experiment Using of Light Quanta Produced by Type-II Parametric Down Conversion[J].Phys.Rev.Lett.,1993 71(24):3893-3897.

[5]G.Weihs,T.Jennewien,C.Simon,A.Zeilinger.Violation of Bell's Inequality under Strict Einstein Locality Conditions[J].Phys.Rev.Lett.,1998 81(23):5039-5043.

[6] M.Aspelmeyer,et al.Long-Distance Free-Space Distribution of Quantum Entanglement[J].Science,2003 301:621-623.

[7] Cheng-zhi Peng,et al.Experimental Free-space Distribution of Entangled Photon Pairs over 13 km:Towards Satellite-Based Global Quantum Communication.[J].Phys.Rev.Lett.,2005 94(15):150501(4).

[8] Xiao-Min Hu,et al.High-Dimensional Bell Test without Detection  Loophole.[J].Phys.Rev.Lett., 129, 060402.