Experimental demonstration on quantum coherence evolution of two-mode squeezed state

Yu Juan; Zhang Yan; Wu Yin-Hua; Yang Wen-Hai; Yan Zhi-Hui; Jia Xiao-Jun

doi:10.7498/aps.72.20221923

Abstract

As one of the most remarkable features of quantum mechanics, quantum coherence is regarded as an important quantum resource in the quantum information processing. The one-mode squeezed state and the two-mode squeezed state (Einstein-Podolsky-Rosen (EPR) entangled states) as the most representative examples of nonclassical states both have quantum coherence. The squeezing property of the squeezed state is described by the variance of quadrature components, and the positive partial transposition (PPT) criterion is used to describe the entanglement of the EPR entangled states. The research of the quantum coherence of Gaussian states is also a bridge between the properties of squeezing and entanglement. It has been shown that the quantum coherence with infinite-dimensional systems can be quantified by relative entropy. One of the widely used effective methods to obtain the value of quantum coherence experimentally is the quantum tomography. The covariance matrices of the quantum states are reconstructed via balanced homodyne detection and then taken into quantum coherence expression to calculate the corresponding value. The main factors affecting quantum coherence are the classical and uncorrelated noise in the actual experimental generation processing and the decoherence effect caused by the coupling between quantum resources and the surrounding environment. And the quantum coherence evolution in the generation and transmission process of the quantum resources is essential for the practical applications. Therefore, we analyze in detail the influences of the impurity of quantum resource on squeezing, entanglement and quantum coherence. The evolutions of quantum coherence of these Gaussian states in the lossy channels are demonstrated experimentally. The quantum coherence is shown to be robust against the loss in the lossy channels, which is similar to the case of squeezing and entanglement. The quantum coherences of the squeezed states and the EPR entangled states are robust against the thermal photons in the actual experimental generation processing, although the squeezing and entanglement of Gaussian states disappear at a certain number of thermal photons. Our research results provide a reference for the practical applications of quantum coherence of the squeezed state and entangled states in the lossy environment.

Keywords:

squeezed state /
Einstein-Podolsky-Rosen entangled states /
purity of quantum state /
quantum coherence

Authors and contacts

1.
School of Optoelectronic Engineering, Xi’an Technological University, Xi’an 710021, China
2.
State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China
3.
Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
4.
China Academy of Space Technology (Xi’an), Xi’an 710000, China

Corresponding author: Yu Juan, yujuan643@126.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 62105256, 62122044, 61925503, 11904218, 12147215, 11834010, 62135008, 62001374, 12004276, 12103039), the Natural Science Research Program of the Education Department of Shaanxi Province, China (Grant Nos. 21JK0694, 18JK0386, 21JY016), the Program for the Innovative Talents of Higher Education Institutions of Shanxi, China, the Scientific and Technological Programs of Higher Education Institutions in Shanxi, China (Grant No. 2019L0794), the Program for Sanjin Scholars of Shanxi Province, China, the Fund for Shanxi “1331Project” Key Subjects Construction, China, and the Natural Science Basic Research Program in Shaanxi Province of China (Grant No. 2021JQ-640).

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References

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[46]	Zhou Y Y, Yu J, Yan Z H, Jia X J, Zhang J, Xie C D, Peng K C 2018 Phys. Rev. Lett. 121 150502 Google Scholar
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Cited By

图 1 实验装置示意图, 其中DBS为双色分束镜; MC为模式清洁器; HWP为半波片; HR为高反镜; PBS为偏振分光棱镜; LO为本地振荡光

Figure 1. Schematic diagram of experimental setup. DBS, dichroic beam splitter; MC, mode cleaner; HWP, half-wave plate; HR, high reflection; PBS, polarizing beam splitter; LO, a strong local oscillator beam.

DownLoad: Full-Size Img PowerPoint

图 2 单模压缩态压缩特性和量子相干性随热光子数的变化　(a) 相对噪声功率; (b) 量子相干性

Figure 2. Dependence of squeezing level and quantum coherence of the one-mode squeezed state on the number of thermal photons: (a) Relative noise power; (b) quantum coherence.

DownLoad: Full-Size Img PowerPoint

图 3 单模压缩态实验结果　(a) 相对噪声功率随传输效率的变化; (b) 损耗信道中压缩态光场的纯度对量子相干性的影响

Figure 3. Experimental results of the one-mode squeezed state in a lossy channel: (a) Dependence of relative noise power on the transmission efficiency; (b) the influence of purity of squeezed state on quantum coherence in a lossy channel.

DownLoad: Full-Size Img PowerPoint

图 4 双模压缩态实验结果　(a) PPT值随热光子数的变化; (b) 量子相干性随热光子数的变化; (c) 纠缠特性随传输效率的变化; (d) 量子相干性随传输效率的变化

Figure 4. Experimental results of the two-mode squeezed states in lossy channels: (a) Dependence of PPT value on the number of thermal photons; (b) dependence of quantum coherence on the number of thermal photons; (c) dependence of PPT values on the transmission efficiency; (d) decoherence of quantum coherence in the lossy channels.

DownLoad: Full-Size Img PowerPoint

[1]	Baumgratz T, Cramer M, Plenio M B 2014 Phys. Rev. Lett. 113 140401 Google Scholar
[2]	Li Y C, Lin H Q 2016 Sci. Rep. 6 26365 Google Scholar
[3]	Shi Y H, Shi H L, Wang X H, Hu M L, Liu S Y, Yang W L, Fan H 2020 J. Phys. A 53 085301 Google Scholar
[4]	Hillery M 2016 Phys. Rev. A 93 012111 Google Scholar
[5]	Napoli C, Bromley T R, Cianciaruso M, Piani M, Johnston N, Adesso G 2016 Phys. Rev. Lett. 116 150502 Google Scholar
[6]	Gisin N, Ribordy G, Tittel W, Zbinden H 2002 Rev. Mod. Phys. 74 145 Google Scholar
[7]	Giovannetti V, Lloyd S, Maccone L 2011 Nat. Photonics 5 222 Google Scholar
[8]	Giorda P, Allegra M 2016 J Phys. A-Math. Theor. 51 2 Google Scholar
[9]	Zhang A, Zhang K, Zhou L, ZhangW 2018 Phys. Rev. Lett. 121 073602 Google Scholar
[10]	Yuan Y, Hou Z, Zhao Y Y, Zhong H S, Xiang G Y, Li C F, Guo G C 2018 Opt. Express 26 004470 Google Scholar
[11]	Wu K D, Hou Z, Zhong H S, Yuan Y, Guo G C 2017 Optica 4 454 Google Scholar
[12]	Zhang M, Kang H J, Wang M H, Xu X L, Peng K C 2021 Photonics Res. 9 887 Google Scholar
[13]	Tan K C, Volkoff T, Kwon H, Jeong H 2017 Phys. Rev. Lett. 119 190405 Google Scholar
[14]	Tan K C, Jeong H 2018 Phys. Rev. Lett. 121 220401 Google Scholar
[15]	Lostaglio M, Müller M P 2019 Phys. Rev. Lett. 123 020403 Google Scholar
[16]	林银, 黄明达, 於亚飞, 张智明 2017 物理学报 66 110301 Google Scholar Lin Y, Huang M D, Yu Y F, Zhang Z M 2017 Acta Phys. Sin. 66 110301 Google Scholar
[17]	Braunstein S L, Caves C M 1994 Phys. Rev. Lett. 72 3439 Google Scholar
[18]	Feng X N, Wei L F 2017 Sci. Rep. 7 15492 Google Scholar
[19]	Zhang Y R, Shao L H, Li Y, Fan H 2016 Phys. Rev. A 93 012334 Google Scholar
[20]	Xu J 2016 Phys. Rev. A 93 032111 Google Scholar
[21]	Buono D, Buono G, Petrillo G, Torre G, Zonzo G, Illuminati F 2016 arXiv: 1609.00913
[22]	周瑶瑶, 刘艳红, 闫智辉, 贾晓军 2021 物理学报 70 104203 Google Scholar Zhou Y Y, Liu Y H 2021 Acta Phys. Sin. 70 104203 Google Scholar
[23]	Yan Z H, Qin J, Qin Z Z, Su X L, Jia X J, Xie C D, Peng K C 2021 Fundamental Research 1 43 Google Scholar
[24]	Chou C W, Hume D B, Thorpe M J, Wineland D J, Rosenband T 2011 Phys. Rev. Lett. 106 160801 Google Scholar
[25]	Huo M R, Qin J L, Cheng J L, Yan Z H, Qin Z Z, Su X L, Jia X J, Xie C D, Peng K C 2018 Sci. Adv. 4 eaas9401 Google Scholar
[26]	Liu S S, Lou Y B, Chen Y X, Jing J T 2022 Phys. Rev. Lett. 128 060503 Google Scholar
[27]	Yan Z H, Wu L, Jia X J, Liu Y H, Deng R J, Li S J, Wang H, Xie C D, Peng K C 2017 Nat. Commun. 8 718 Google Scholar
[28]	Ma L X, Lei X, Yan J L, Li R Y, Chai T, Yan Z H, Jia X J, Xie C D, Peng K C 2022 Nat. Commun. 13 2368 Google Scholar
[29]	Lei X, Ma L X, Yan J L, Zhou X Y, Yan Z H, Jia X J 2022 Adv. Phys. X 7 2060133 Google Scholar
[30]	Liu S S, Lou Y B, Xin J, Jing J T 2018 Phys. Rev. Appl. 10 064046 Google Scholar
[31]	Liu Y H, Huo N, Li J M, Cui L, Li X Y, Ou Z Y 2019 Opt. Express 27 11292 Google Scholar
[32]	Yu J, Qin Y, Qin J L, Wang H, Yan Z H, Jia X J, Peng K C 2020 Phys. Rev. Appl. 13 024037 Google Scholar
[33]	Goda K, Miyakawa O, Mikhailov E E, Saraf S, Adhikari R, McKenzie K, Ward R, Vass S, Weinstein A J, Mavalvala N 2008 Nat. Phys. 4 472 Google Scholar
[34]	Guo X S, Breum C R, Borregaard J, Izumi S, Larsen M V, Gehring T, Christandl M, Neergaard-Nielsen J S, Andersen U L 2020 Nat. Phys. 16 281 Google Scholar
[35]	Bai S Y, An J H 2021 Phys. Rev. Lett. 127 083602 Google Scholar
[36]	Yan Z H, Wu L, Jia X J, Xie C D, Peng K C 2021 Adv. Quantum Technol. 4 2100071 Google Scholar
[37]	Streltsov A, Singh U, Dhar H S, Bera M N, Adesso G 2015 Phys. Rev. Lett. 115 020403 Google Scholar
[38]	Chitambar E, Hsieh M H 2016 Phys. Rev. Lett. 117 020402 Google Scholar
[39]	Deng X W, Liu Y, Wang M H, Su X L, Peng K C 2021 npj Quantum Inform. 7 65 Google Scholar
[40]	Liu Y, Zheng K M, Kang H J, Han D M, Wang M H, Zhang L J, Su X L, Peng K C 2022 npj Quantum Inform. 8 38 Google Scholar
[41]	Kang H J, Han D M, Wang N, Liu Y, Hao S H, Su X L 2021 Photonics Res. 9 1330 Google Scholar
[42]	Weedbrook C, Pirandola S, García-Patrón R, Cerf N J, Ralph T C, Shapiro J H, Lloyd S 2012 Rev. Mod. Phys. 84 621 Google Scholar
[43]	Takeno Y, Yukawa M, Yonezawa H, Furusawa A 2007 Opt. Express 15 4321 Google Scholar
[44]	Adesso G, Serafini A 2004 Phys. Rev. A 70 022318 Google Scholar
[45]	Ou Z Y, Pereira S F, Kimble H J, Peng K C 1992 Phys. Rev. Lett. 68 3663 Google Scholar
[46]	Zhou Y Y, Yu J, Yan Z H, Jia X J, Zhang J, Xie C D, Peng K C 2018 Phys. Rev. Lett. 121 150502 Google Scholar
[47]	Bougouffa S, Ficek Z 2020 Phys. Rev. A 102 043720 Google Scholar
[48]	Xiong S J, Sun Z, Su Q P, Xi Z J, Yang C P 2021 Optica 8 1003 Google Scholar

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Vol. 72, Issue 3 - 2023-02-05

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