优化抽运空间分布实现连续变量超纠缠的纠缠增强
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摘要
超纠缠近年来受到人们广泛的关注,其在量子信息和量子通信领域具有非常重要的作用.在Liu等(2014 Phys. Rev. Lett. 113 170501)的工作中,他们利用二类相位匹配的非简并光学参量放大器获得了约1.00 dB的同时具有轨道角动量和自旋角动量纠缠的连续变量超纠缠态.在此基础上,本文通过进一步分析抽运模式与下转换模式间的纠缠关系,优化了抽运空间构造.实验结果表明,相比Liu等利用高斯基模做抽运场,使用优化的抽运模式时轨道角动量纠缠和自旋角动量纠缠的不可分度分别提高了96.2%和96.3%,最终将超纠缠态的纠缠度提高到了(4.00±0.02) dB,为连续变量超纠缠态的进一步应用奠定了基础.
In recent years, more and more researchers have paid attention to the hyperentanglement, because it plays a very important role in the quantum information and quantum communication. Continuous-variable hyperentangled state with orbital angular momentum and spin angular momentum has a promising application in the parallel processing of continuous-variable multi-channel quantum information and multiparameters quantum metrology. Recently Liu et al.(2014 Phys. Rev. Lett. 113 170501) have produced a quantum correlation of about 1.00 dB for the continuous-variable hyperentangled state by a type-II non-degenerate optical parametric amplifier. The generation of continuous-variable hyperentangled state is affected by the mode matching between the pump field and the down-conversion field, since the hyperentanglement contains spatial high-order transverse mode entanglement. In the present paper, we first theoretically analyze the relationship between the pump and the two down-conversion modes and demonstrate the dependence of the inseparability on normalized pump power for the different pump modes. Hence, we find that the optimal pump mode is the superposition of LG00 mode and LG01 mode. However, the optimal pump mode is rather complicated and difficult to experimentally generate, in the alternative scheme the LG01 mode is used as the pump field to obtain the optimal entanglement. In the experiment, the LG01 mode is produced by converting the HG11 mode with aπ/2 converter, and here the HG11 mode is achieved by tailoring the fundamental mode with a four-quadrant phase mask and a filtering cavity. Then the LG0 0 mode or LG0 1 mode is used as the pump field to drive the nondegenerate optical parametric amplifier operating in spatial multimode. When the non-degenerate optical parametric amplifier is operated in the de-amplification, the hyperentanglement with orbital angular momentum and spin angular momentum is produced. The output entangled beams pass through polarization beam splitter and are analyzed by using the balanced homodyne detection systems with the local oscillator operating in the HG01 and HG10. The noise of the phase quadrature or the amplitude quadrature is obtained, when the relative phase between the local oscillator and the signal beam is locked to π/2 or 0. Then the quantum correlations of orbital angular momentum and spin angular momentum can be deduced. The experimental results show that the continuous-variable hyperentanglement of light with a quantum correlation of(4.00 ± 0.02) dB is produced.Compared with the results of Liu et al. obtained by using the LG0 0 mode, the inseparability of orbital angular momentum and spin angular momentum entanglement are enhanced by approximately 96.2% and 96.3%,respectively, through using the LG0 1 mode. Such a continuous-variable hyperentanglement may have promising applications in high-dimensional quantum information and multi-dimensional quantum measurement, and this approach is potentially extended to a discrete variable domain.
In recent years, more and more researchers have paid attention to the hyperentanglement, because it plays a very important role in the quantum information and quantum communication. Continuous-variable hyperentangled state with orbital angular momentum and spin angular momentum has a promising application in the parallel processing of continuous-variable multi-channel quantum information and multiparameters quantum metrology. Recently Liu et al.(2014 Phys. Rev. Lett. 113 170501) have produced a quantum correlation of about 1.00 dB for the continuous-variable hyperentangled state by a type-II non-degenerate optical parametric amplifier. The generation of continuous-variable hyperentangled state is affected by the mode matching between the pump field and the down-conversion field, since the hyperentanglement contains spatial high-order transverse mode entanglement. In the present paper, we first theoretically analyze the relationship between the pump and the two down-conversion modes and demonstrate the dependence of the inseparability on normalized pump power for the different pump modes. Hence, we find that the optimal pump mode is the superposition of LG00 mode and LG01 mode. However, the optimal pump mode is rather complicated and difficult to experimentally generate, in the alternative scheme the LG01 mode is used as the pump field to obtain the optimal entanglement. In the experiment, the LG01 mode is produced by converting the HG11 mode with aπ/2 converter, and here the HG11 mode is achieved by tailoring the fundamental mode with a four-quadrant phase mask and a filtering cavity. Then the LG0 0 mode or LG0 1 mode is used as the pump field to drive the nondegenerate optical parametric amplifier operating in spatial multimode. When the non-degenerate optical parametric amplifier is operated in the de-amplification, the hyperentanglement with orbital angular momentum and spin angular momentum is produced. The output entangled beams pass through polarization beam splitter and are analyzed by using the balanced homodyne detection systems with the local oscillator operating in the HG01 and HG10. The noise of the phase quadrature or the amplitude quadrature is obtained, when the relative phase between the local oscillator and the signal beam is locked to π/2 or 0. Then the quantum correlations of orbital angular momentum and spin angular momentum can be deduced. The experimental results show that the continuous-variable hyperentanglement of light with a quantum correlation of(4.00 ± 0.02) dB is produced.Compared with the results of Liu et al. obtained by using the LG0 0 mode, the inseparability of orbital angular momentum and spin angular momentum entanglement are enhanced by approximately 96.2% and 96.3%,respectively, through using the LG0 1 mode. Such a continuous-variable hyperentanglement may have promising applications in high-dimensional quantum information and multi-dimensional quantum measurement, and this approach is potentially extended to a discrete variable domain.
引文
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[13]Liu K,Guo J,Cai C X,Guo S F,Gao J R 2014 Phys.Rev.Lett.113 170501
[14]Yang Y,Li F L 2009 Phys.Rev.A 80 022315
[15]Lee S Y,Ji S W,Kim H J,Nha H 2011 Phys.Rev.A 84012302
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[17]Yan Z H,Jia X J,Su X L,Duan Z Y,Xie C D,Peng K C2012 Phys.Rev.A 85 040305
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[24]Martinelli M,Huguenin J A O,Nussenzveig P,Khoury A Z2004 Phys.Rev.A 70 013812
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[26]Duan L M,Giedke G,Cirac J I,Zoller P 2000 Phys.Rev.Lett.84 2722
[27]Simon R 2000 Phys.Rev.Lett.84 2726
[28]Lassen M,Delaubert V,Janousek J,Wagner K,Bachor H,Lam P K,Treps N,Buchhave P,Fabre C,Harb C C 2007Phys.Rev.Lett.98 083602
[29]Taylor M A,Janousek J,Daria V,Knittel J,Hage B,Bachor H,Bowen W P 2013 Nat.Photon.7 229
[2]Jing J T,Zhang J,Yan Y,Zhao F G,Xie C D,Peng K C 2003 Phys.Rev.Lett.90 167903
[3]Giovannetti V,Lloyd S,Maccone L 2004 Science 306 1330
[4]Alexander R N,Wang P,Sridhar N,Chen M,Pfister O,Menicucci N C 2016 Phys.Rev.A 94 032327
[5]Kwiat P G 1997 J.Mod.Opt.44 2173
[6]Barreiro J T,Wei T,Kwiat P G 2008 Nat.Phys.4 282
[7]Schuck C,Huber G,Kurtsiefer C,Weinfurter H 2006 Phys.Rev.Lett.96 190501
[8]Chen K,Li C M,Zhang Q,Chen Y A,Goebel A,Chen S,Mair A,Pan J W 2007 Phys.Rev.Lett.99 120503
[9]Gao W B,Xu P,Yao X C,Gühne O,Cabello A,Lu C Y,Peng C Z,Chen Z B,Pan J W 2010 Phys.Rev.Lett.104020501
[10]Barreiro J T,Langford N K,Peters N A,Kwiat P G 2005Phys.Rev.Lett.95 260501
[11]Wang X L,Luo Y H,Huang H L,Chen M C,Su Z E,Liu C,Chen C,Li W,Fang Y Q,Jiang X,Zhang J,Li L,Liu N L,Lu C Y,Pan J W 2018 Phys.Rev.Lett.120 260502
[12]Coutinho dos Santos B,Dechoum K,Khoury A Z 2009 Phys.Rev.Lett.103 230503
[13]Liu K,Guo J,Cai C X,Guo S F,Gao J R 2014 Phys.Rev.Lett.113 170501
[14]Yang Y,Li F L 2009 Phys.Rev.A 80 022315
[15]Lee S Y,Ji S W,Kim H J,Nha H 2011 Phys.Rev.A 84012302
[16]Hu L Y,Liao Z Y,Zubairy M S 2017 Phys.Rev.A 95 012310
[17]Yan Z H,Jia X J,Su X L,Duan Z Y,Xie C D,Peng K C2012 Phys.Rev.A 85 040305
[18]Xin J,Qi J,Jing J T 2017 Opt.Lett.42 366
[19]Liu K,Guo J,Cai C X,Zhang J X,Gao J R 2016 Opt.Lett.41 5178
[20]Lassen M,Delaubert V,Harb C C,Lam P K,Treps N,Bachor H 2006 J.Eur.Opt.Soc.1 06003
[21]Guo J,Cai C X,Ma L,Liu K,Sun H X,Gao J R 2017 Opt.Express 25 4985
[22]Navarrete-Benlloch C,Roldán E,de Valcárcel G J 2008 Phys.Rev.Lett.100 203601
[23]Beijersbergen M W,Allen L,van der Veen H E L O,Woerdman J P 1993 Opt.Commun.96 123
[24]Martinelli M,Huguenin J A O,Nussenzveig P,Khoury A Z2004 Phys.Rev.A 70 013812
[25]Abramochkin E,Volostnikov V 1991 Opt.Commum.83 123
[26]Duan L M,Giedke G,Cirac J I,Zoller P 2000 Phys.Rev.Lett.84 2722
[27]Simon R 2000 Phys.Rev.Lett.84 2726
[28]Lassen M,Delaubert V,Janousek J,Wagner K,Bachor H,Lam P K,Treps N,Buchhave P,Fabre C,Harb C C 2007Phys.Rev.Lett.98 083602
[29]Taylor M A,Janousek J,Daria V,Knittel J,Hage B,Bachor H,Bowen W P 2013 Nat.Photon.7 229
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