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Continuous variable (CV) quantum squeezed state and entangled state are important quantum resources, which have been widely used in quantum communication, quantum metrology and quantum computation. In recent years, people have paid much attention to the multi-mode optical parametric amplifier (OPO) process because the multi-mode non-classical light field is able to construct the multiplexing quantum information system for improving the working efficiency and channel capacity. As a special multi-mode optical field, optical frequency comb has been used in optical frequency measurement, atomic spectroscopy and frequency-division multiplex-based communication. Especially, there are a number of notable researches where quantum frequency combs are used, which exhibit multimode-entangled photon states. The quantum frequency combs provide a promising platform for quantum information technology based on time-bin-encoded qubits. In this paper, the entanglement characteristics of frequency comb in type II nondegenerate optical parametric amplifier (NOPA) below threshold are investigated experimentally. The bipartite entanglement with frequency comb structure between idle light (
$\hat a_{{\rm{i}}, + n\varOmega }^{{\rm{out}}}$ ) and signal light($\hat a_{{\rm{s}}, + n\varOmega }^{{\rm{out}}}$ ) is generated by the NOPA whose free spectral range (Ω) is 1.99 GHz operated in the de-amplification state and then analyzed by dual balanced homodyne detection system (BHD) with different values of frequency$\omega \pm n\varOmega $ (n = 0, 1, 2). The local light of BHD with frequency$\omega \pm n\varOmega $ is generated by the fiber intensity modulator and tailored by the mode cleaner. Here, we measure the correlation noise of side and frequency combs normalized to the shot noise limit relating to the phase of local oscillator beam, and we show the correlation noise of$\hat a_{\rm{i}}^{{\rm{out}}}$ and$\hat a_{\rm{s}}^{{\rm{out}}}$ , the correlation noise of$\hat a_{{\rm{i}}, + \varOmega }^{{\rm{out}}}$ and$\hat a_{{\rm{s}}, - \varOmega }^{{\rm{out}}}$ , the correlation noise of$\hat a_{{\rm{i}}, - \varOmega }^{{\rm{out}}}$ and$\hat a_{{\rm{s}}, + \varOmega }^{{\rm{out}}}$ , the correlation noise of$\hat a_{{\rm{i}}, + 2\varOmega }^{{\rm{out}}}$ and$\hat a_{{\rm{s}}, - 2\varOmega }^{{\rm{out}}}$ and the correlation noise of$\hat a_{{\rm{i}}, - 2\varOmega }^{{\rm{out}}}$ and$\hat a_{{\rm{s}}, + 2\varOmega }^{{\rm{out}}}$ . The experimental results show that the five pairs of entangled states with 4.5 dB entanglement are simultaneously produced by a type II OPO. Next, we can redesign NOPA to reduce its free spectral range and intracavity loss, and prepare local light with a high-order sideband frequency by fiber modulators with high bandwidth, it promises to obtain huge multiple bipartite entangled states. As a kind of extensible quantum information system, the frequency comb CV entanglement can be used to provide a necessary light source for realizing the experiment of frequency division multiplexing multi-channel teleportation, which lays a foundation for the future large-capacity quantum communication and network.[1] Furusawa A, Sorensen J L, Braustein S L, Fuchs C A, Kimble H J, Polzik E S 1998 Science 282 706
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[2] Raussendorfand R, Briegel H J 2001 Phys. Rev. Lett. 86 5188
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[3] Brida G, Genovese M, Berchera I R 2010 Nat. Photonics 4 227
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[4] D’Ambrosio V, Spagnolo N, Del Re L, Slussarenko S, Li Y, Kwek L C, Marrucci L, Walborn S P, Aolita L, Sciarrino F 2013 Nat. Commun. 4 2432
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[5] 闫子华, 孙恒信, 蔡春晓, 马龙, 刘奎, 郜江瑞 2017 物理学报 66 114205
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Yan Z H, Sun H X, Cai C X, Ma L, Liu K, Gao J R 2017 Acta Phys. Sin. 66 114205
Google Scholar
[6] Ma L, Guo H, Liu K, Sun H X, Gao J R 2019 Opt. Express 27 35120
Google Scholar
[7] Lassen M, Delaubert V, Janousek J, Wagner K, Bachor H A, Lam P K, Treps N, Buchhave P, Fabre C, Harb C C 2007 Phys. Rev. Lett. 98 083602
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[8] Weedbrook C, Pirandola S, García-Patrón R, Cerf N J, Ralph T C, Shapiro J H, Lloyd S 2012 Rev. Mod. Phys. 84 621
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[9] Liu K, Guo J, Cai C X, Guo S F, Gao J R 2014 Phys. Rev. Lett. 113 170501
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Google Scholar
[11] Cai C X, Ma L, Li J, Guo H, L iu, Sun H X, Yang R G, Gao J G 2018 Photonics Res. 6 479
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[12] 李娟, 李佳明, 蔡春晓, 孙恒信, 刘奎, 郜江瑞 2019 物理学报 68 034204
Google Scholar
Li J, Li J M, Cai C X, Sun H X, Liu K, Gao J R 2019 Acta Phys. Sin. 68 034204
Google Scholar
[13] Menicucci N C, Flammia S T, Pfister O 2008 Phys. Rev. Lett. 101 130501
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[14] Dunlop A E, Huntington E H 2006 Phys. Rev. A 73 013817
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[15] Heurs M, Webb J G, Dunlop A E, Harb C C, Ralph T C, Huntington E H 2010 Phys. Rev. A 81 032325
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[16] Pysher M, Miwa Y, Shahrokhshahi R, Bloomer R, Pfister O 2011 Phys. Rev. Lett. 107 030505
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[17] Chen M, Menicucci N C, Pfister O 2014 Phys. Rev. Lett. 112 120505
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[18] Pinel O, Jian P, Medeiros de Araújo R, Feng J X, Chalopin B, Fabre C, Treps N 2012 Phys. Rev. Lett. 108 083601
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[19] Roslund J, Medeiros de Araújo R, Jiang S, Fabre C, Treps N 2014 Nat. Photonics 8 109
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[20] Ra Y S, Dufour A, Walschaers M, Jacquard C, Michel T, Fabre C, Treps N 2019 Nat. Phys. 16 144
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[22] Song H B, Yonezawa H, Kuntz K B, Heurs M, Huntington E H 2014 Phys. Rev. A 90 042337
[23] Duan L M, Giedke G, Cirac J I, Zoller P 2000 Phys. Rev. Lett. 84 2722
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[24] Simon R 2000 Phys. Rev. Lett. 84 2726
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[25] Yang R G, Zhang J, Zhai Z H, Zhai S Q, Liu K, Gao J R 2015 Opt. Express 23 021323
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图 1 光学频率梳
Figure 1. Optical frequency combs.
图 2 实验装置图(RF, 射频源; MC, 模式清洁器; PZT, 压电陶瓷; HWP, 半波片; PBS, 偏振分光棱镜; BHD, 平衡零拍系统; SA, 频谱分析仪; EOM, 光纤强度调制器)
Figure 2. Experimental setup. RF, radio-frequency signal generator; MC, mode cleaner; PZT, piezoelectric transducer; HWP, half wave plate; PBS, polarizing beam splitter; BHD, balanced homodyne detector; SA, spectrum analyzer; EOM, fiber intensity modulator.
图 3 不同频率梳边带处的关联噪声随本地光相位变化的归一化噪声功率曲线(其中蓝线为散粒噪声基准, 绿线为关联噪声谱) (a)
$\hat a_{\rm{i}}^{{\rm{out}}}$ 与$\hat a_{\rm{s}}^{{\rm{out}}}$ 的关联测量结果; (b)$\hat a_{{\rm{i, }} + \varOmega }^{{\rm{out}}}$ 与$\hat a_{{\rm{s}}, - \varOmega }^{{\rm{out}}}$ 的关联测量结果; (c)$\hat a_{{\rm{i}}, - \varOmega }^{{\rm{out}}}$ 与$\hat a_{{\rm{s}}, + \varOmega }^{{\rm{out}}}$ 的关联测量结果; (d)$\hat a_{{\rm{i, }} + 2\varOmega }^{{\rm{out}}}$ 与$\hat a_{{\rm{s}}, - 2\varOmega }^{{\rm{out}}}$ 的关联测量结果; (e)$\hat a_{{\rm{i}}, - 2\varOmega }^{{\rm{out}}}$ 与$\hat a_{{\rm{s}}, + 2\varOmega }^{{\rm{out}}}$ 的关联测量结果; 谱仪的分析频率为3 MHz, 分辨率带宽为300 kHz, 视频带宽为1 kHzFigure 3. The correlation noise of sideband frequency combs normalized to the shot noise limit depending on the phase of local oscilla-tor beam (the blue light is shot noise limit, the green light is correlation noise): (a) The correlation noise of
$\hat a_{\rm{i}}^{{\rm{out}}}$ and$\hat a_{\rm{s}}^{{\rm{out}}}$ ; (b) the correlation noise of$\hat a_{{\rm{i, }} + \varOmega }^{{\rm{out}}}$ and$\hat a_{{\rm{s}}, - \varOmega }^{{\rm{out}}}$ ; (c) the correlation noise of$\hat a_{{\rm{i}}, - \varOmega }^{{\rm{out}}}$ and$\hat a_{{\rm{s}}, + \varOmega }^{{\rm{out}}}$ ; (d) the correlation noise of$\hat a_{{\rm{i, }} + 2\varOmega }^{{\rm{out}}}$ and$\hat a_{{\rm{s}}, - 2\varOmega }^{{\rm{out}}}$ ; (e) the correlation noise of$\hat a_{{\rm{i}}, - 2\varOmega }^{{\rm{out}}}$ and$\hat a_{{\rm{s}}, + 2\varOmega }^{{\rm{out}}}$ . The analysis frequency of 3 MHz with resolution bandwidth of 300 kHz and video bandwidth of 1 kHz. -
[1] Furusawa A, Sorensen J L, Braustein S L, Fuchs C A, Kimble H J, Polzik E S 1998 Science 282 706
Google Scholar
[2] Raussendorfand R, Briegel H J 2001 Phys. Rev. Lett. 86 5188
Google Scholar
[3] Brida G, Genovese M, Berchera I R 2010 Nat. Photonics 4 227
Google Scholar
[4] D’Ambrosio V, Spagnolo N, Del Re L, Slussarenko S, Li Y, Kwek L C, Marrucci L, Walborn S P, Aolita L, Sciarrino F 2013 Nat. Commun. 4 2432
Google Scholar
[5] 闫子华, 孙恒信, 蔡春晓, 马龙, 刘奎, 郜江瑞 2017 物理学报 66 114205
Google Scholar
Yan Z H, Sun H X, Cai C X, Ma L, Liu K, Gao J R 2017 Acta Phys. Sin. 66 114205
Google Scholar
[6] Ma L, Guo H, Liu K, Sun H X, Gao J R 2019 Opt. Express 27 35120
Google Scholar
[7] Lassen M, Delaubert V, Janousek J, Wagner K, Bachor H A, Lam P K, Treps N, Buchhave P, Fabre C, Harb C C 2007 Phys. Rev. Lett. 98 083602
Google Scholar
[8] 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
[9] Liu K, Guo J, Cai C X, Guo S F, Gao J R 2014 Phys. Rev. Lett. 113 170501
Google Scholar
[10] Liu K, Guo J, Cai C X, Zhang J X, Gao J R 2016 Opt. Lett. 41 5178
Google Scholar
[11] Cai C X, Ma L, Li J, Guo H, L iu, Sun H X, Yang R G, Gao J G 2018 Photonics Res. 6 479
Google Scholar
[12] 李娟, 李佳明, 蔡春晓, 孙恒信, 刘奎, 郜江瑞 2019 物理学报 68 034204
Google Scholar
Li J, Li J M, Cai C X, Sun H X, Liu K, Gao J R 2019 Acta Phys. Sin. 68 034204
Google Scholar
[13] Menicucci N C, Flammia S T, Pfister O 2008 Phys. Rev. Lett. 101 130501
Google Scholar
[14] Dunlop A E, Huntington E H 2006 Phys. Rev. A 73 013817
Google Scholar
[15] Heurs M, Webb J G, Dunlop A E, Harb C C, Ralph T C, Huntington E H 2010 Phys. Rev. A 81 032325
Google Scholar
[16] Pysher M, Miwa Y, Shahrokhshahi R, Bloomer R, Pfister O 2011 Phys. Rev. Lett. 107 030505
Google Scholar
[17] Chen M, Menicucci N C, Pfister O 2014 Phys. Rev. Lett. 112 120505
Google Scholar
[18] Pinel O, Jian P, Medeiros de Araújo R, Feng J X, Chalopin B, Fabre C, Treps N 2012 Phys. Rev. Lett. 108 083601
Google Scholar
[19] Roslund J, Medeiros de Araújo R, Jiang S, Fabre C, Treps N 2014 Nat. Photonics 8 109
Google Scholar
[20] Ra Y S, Dufour A, Walschaers M, Jacquard C, Michel T, Fabre C, Treps N 2019 Nat. Phys. 16 144
[21] Yang R G, Zhang J, Zhai S Q, Liu K, Zhang J X, Gao J R 2013 J. Opt. Soc. Am. B 30 314
Google Scholar
[22] Song H B, Yonezawa H, Kuntz K B, Heurs M, Huntington E H 2014 Phys. Rev. A 90 042337
[23] Duan L M, Giedke G, Cirac J I, Zoller P 2000 Phys. Rev. Lett. 84 2722
Google Scholar
[24] Simon R 2000 Phys. Rev. Lett. 84 2726
Google Scholar
[25] Yang R G, Zhang J, Zhai Z H, Zhai S Q, Liu K, Gao J R 2015 Opt. Express 23 021323
Google Scholar
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