Deterministic quantum entanglement among multiple quantum nodes

Liu Yan-Hong; Wu Liang; Yan Zhi-Hui; Jia Xiao-Jun; Peng Kun-Chi

doi:10.7498/aps.68.20181614

Abstract

Quantum entanglement is a significant quantum resource, which plays a central role in quantum communication. For realizing quantum information network, it is important to establish deterministic quantum entanglement among multiple spatial-separated quantum memories, and then the stored entanglement is transferred into the quantum channels for distributing and transmitting the quantum information at the user-control time. Firstly, we introduce the scheme of deterministic generation polarization squeezed state at 795 nm. A pair of quadrature amplitude squeezed optical fields are prepared by two degenerate optical parameter amplifiers pumped by a laser at 398 nm, and then the polarization squeezed state of light appears by combining the generated two quadrature amplitude squeezed optical beams on a polarizing beam splitter. Secondly, we present the experimental demonstration of tripartite polarization entanglement described by Stokes operators of optical field. The quadrature tripartite entangled states of light corresponding to the resonance with D1 line of rubidium atoms are transformed into the continuous-variable polarization entanglement via polarization beam splitter with three bright local optical beams. Finally, we propose the generation, storage and transfer of deterministic quantum entanglement among three spatially separated atomic ensembles. By the method of electromagnetically induced transparency light-matter interaction, the optical multiple entangled state is mapped into three distant atomic ensembles to build the entanglement among three atomic spin waves. Then, the quantum noise of entanglement stored in the atomic ensembles is transferred to the three space-seperated quadrature entangled light fields through three quantum channels. The existence of entanglement among the three released beams verifies that the system has the ability to maintain the multipartite entanglement. This protocol realizes the entanglement among three distant quantum nodes, and it can be extended to quantum network with more quantum nodes. All of these lay the foundation for realizing the large-scale quantum network communication in the future.

Keywords:

deterministic quantum entanglement /
electromagnetically induced transparency /
multipartite entanglement /
quantum nodes

Authors and contacts

1.
Institute of Opto-Electronics, State Key Laboratory of Quantum Optics and Quantum Optics Devices, Shanxi University, Taiyuan 030006, China
2.
Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China

Corresponding author: Jia Xiao-Jun, jiaxj@sxu.edu.cn

Funds: Project supported by the National Key R&D Program of China (Grant No. 2016YFA0301402), the National Natural Science Foundation of China (Grant Nos. 61775127, 11474190, 11654002), the Program for Sanjin Scholars of Shanxi Province, China, the Shanxi Scholarship Council of China, and the Fund for Shanxi “1331 Project” Key Subjects Construction, China.

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References

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Cited By

图 1 偏振压缩光场制备原理图

Figure 1. Schematic of generation system of polarization squeezing.

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图 2 Stokes分量(a) ${\hat S_0}$, (b) ${\hat S_1}$, (c)${\hat S_2}$, (d) ${\hat S_3}$的量子噪声的实验测量(HWP, 二分之一波片; QWP, 四分之一波片; PBS, 偏振分束棱镜; +/−, 功率加法/减法器)

Figure 2. Measurement of quantum noise of Stokes component (a) ${\hat S_0}$, (b) ${\hat S_1}$, (c) ${\hat S_2}$, (d) ${\hat S_3}$. HWP, half-wave plate; QWP, quarter-wave plate; PBS, polarization beam splitter; +/−, positive/negative power combiner.

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图 3 偏振压缩光Stokes分量的量子噪声^[61]　(a) ${\hat S_0}$; (b) $\hat S{}_1$; (c) ${\hat S_2}$; (d) ${\hat S_3}$

Figure 3. Quantum noises of Stokes component of polarization squeezedlight^[61]: (a) ${\hat S_0}$; (b) ${\hat S_1}$; (c) ${\hat S_2}$; (d) ${\hat S_3}$.

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图 4 偏振纠缠制备原理图

Figure 4. Schematic for the generation system of polarization entanglement.

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图 5 三组分偏振纠缠态产生方案(BS1, 光学分束器1; BS2, 光学分束器2; PBS1, 偏振分束棱镜1; PBS2, 偏振分束棱镜2; PBS3, 偏振分束棱镜3)

Figure 5. Schematic for the generation of tripartite polarization entangled state. BS1, beam splitter1; BS2, beam splitter2; PBS1, polarization beam splitter1; PBS2, polarization beam splitter2; PBS3, polarization beam splitter3.

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图 6 分析频率在1—6 MHz间测量的Stokes关联方差　(a) ${{\text{δ }}^2}({\hat S_{{2_{{d_2}}}}} - {\hat S_{{2_{{d_3}}}}})$; (b) ${{\text{δ }}^2}({g_1}{\hat S_{{3_{{d_1}}}}} + {\hat S_{{3_{{d_2}}}}} + {\hat S_{{3_{d3}}}})$; (c) ${{\text{δ }}^2}({\hat S_{{2_{{d_1}}}}} - {\hat S_{{2_{d3}}}})$; (d) ${{\text{δ }}^2}({\hat S_{{3_{{d_1}}}}} + {g_2}{\hat S_{{3_{{d_2}}}}} + {\hat S_{{3_{d3}}}})$; (e) ${{\text{δ }}^2}({\hat S_{{2_{{d_1}}}}} - {\hat S_{{2_{d2}}}})$; (f) ${{\text{δ }}^2}({\hat S_{{3_{{d_1}}}}} + {\hat S_{{3_{{d_2}}}}} + {g_3}{\hat S_{{3_{d3}}}})$

Figure 6. Measured correlation variances of (a) ${{\text{δ }}^2}({\hat S_{{2_{{d_2}}}}} - {\hat S_{{2_{{d_3}}}}})$, (b) ${{\text{δ }}^2}({g_1}{\hat S_{{3_{{d_1}}}}} + {\hat S_{{3_{{d_2}}}}} + {\hat S_{{3_{d3}}}})$, (c) ${{\text{δ }}^2}({\hat S_{{2_{{d_1}}}}} - {\hat S_{{2_{d3}}}})$, (d) ${{\text{δ }}^2}({\hat S_{{3_{{d_1}}}}} + {g_2}{\hat S_{{3_{{d_2}}}}} + {\hat S_{{3_{d3}}}})$, (e) ${{\text{δ }}^2}({\hat S_{{2_{{d_1}}}}} - {\hat S_{{2_{d2}}}})$, (f) ${{\text{δ }}^2}({\hat S_{{3_{{d_1}}}}} + {\hat S_{{3_{{d_2}}}}} + {g_3}{\hat S_{{3_{d3}}}})$ over the analysis frequency rangefrom 1 to 6 MHz.

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图 7 原子系综纠缠示意图

Figure 7. Schematic of atom-atom entanglement generation system.

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图 8 三原子系综纠缠实验装置图

Figure 8. Experimental device diagram of quantum entanglement among three distant atomic ensembles.

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图 9 信号光与控制光的时序控制图

Figure 9. Sequence control of signal and control light.

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图 10 测量的输入模式和释放模式的关联方差

Figure 10. Measured normalized correlation variances of input and released optical submodes.

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表 1 释放光模正交分量不同组合的归一化关联方差

Table 1. Values of normalized correlation variances for different combinations.

不同组合的关联方差	输入模式/dB	原子自旋波/dB	释放模式/dB
$\left\langle {{{\text{δ}}^2}({{\hat X}_2} - {{\hat X}_3})} \right\rangle $	−3.30 ± 0.05	−0.56 ± 0.03	−0.37 ± 0.03
$\left\langle {{{\text{δ}}^2}({g_1}{{\hat P}_1} + {{\hat P}_2} + {{\hat P}_3})} \right\rangle $	−2.93 ± 0.05	−0.15 ± 0.02	−0.10 ± 0.02
$\left\langle {{{\text{δ}}^2}({{\hat X}_1} - {{\hat X}_3})} \right\rangle $	−3.25 ± 0.05	−0.53 ± 0.03	−0.35 ± 0.03
$\left\langle {{{\text{δ}}^2}({{\hat P}_1} + {g_2}{{\hat P}_2} + {{\hat P}_3})} \right\rangle $	−2.91 ± 0.05	−0.15 ± 0.02	−0.10 ± 0.02
$\left\langle {{{\text{δ}}^2}({{\hat X}_1} - {{\hat X}_2})} \right\rangle $	−3.25 ± 0.05	−0.52 ± 0.03	−0.34 ± 0.03
$\left\langle {{{\text{δ}}^2}({g_1}{{\hat P}_2} + {{\hat P}_2} + {{\hat P}_3})} \right\rangle $	−2.90 ± 0.05	−0.14 ± 0.02	−0.09 ± 0.02

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[1]	Pan J W, Chen Z B, Lu C Y, Weinfurter H, Zeilinger A, Żukowski M 2012 Rev. Mod. Phys. 84 777 Google Scholar
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[19]	Yan Z H, Jia X J 2017 Quantum Sci. Technol. 2 024003 Google Scholar
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[26]	Fiore V, Yang Y, Kuzyk M C, Barbour R, Tian L, Wang H 2011 Phys. Rev. Lett. 107 133601 Google Scholar
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