微波连续变量极化纠缠
|
摘要
极化微波作为当前被广泛应用的信息载体,具有许多独特的优势.随着超导技术的发展,量子微波技术逐渐兴起,将量子纠缠应用于极化微波将具有广阔的应用前景.本文阐述了连续变量极化纠缠的原理,提出了极化纠缠微波方案并进行了仿真分析,利用归一化的不可分度I作为判据,分析了在整个约瑟夫森混合器100 MHz工作带宽内斯托克斯参量的不可分度I(S_1,S_2),I(S_2,S_3),并进一步分析了I分别与压缩度r、振幅比值Q的关系,发现I(S_1,S_2),I(S_2,S_3)分别对振幅比值Q、压缩度r的变化敏感,且在本文研究的条件下I(S_1,S_2)始终大于1,I(S_2,S_3)始终小于1,斯托克斯参量S_2,S_3构成不可分态,方案产生的两个微波信号E_a和E_b存在二组分极化纠缠,最佳纠缠出现在70 MHz附近,此时I(S_2,S_3)取得最小值0.25.
As a widely utilized information carrier, polarization microwave shows plenty of merits. Quantum microwave is booming gradually due to the development of superconducting technology, which makes it a promising potential to apply quantum entanglement to polarization microwave. In this paper, we introduce the concept of continuous variable polarization entanglement. Meanwhile, a scheme of polarization entanglement in microwave domain is proposed and simulated. The detail derivations are given and discussed. Polarization entangled microwaves are prepared by combining quadrature entangled signals and strong coherent signals on polarization beam splitters, and quadrature entangled signals are prepared by utilizing Josephson mixer. In order to probe the polarization entanglement between output signals, inseparability of Stokes vectors I(S_1,S_2)and I(S_2,S_3),is analyzed in 100 MHz operation bandwidth of Josephson mixer. The relation between inseparability I and squeezing degree r and between inseparability I and amplitude ratio Q are analyzed respectively. The results show that I(S_1,S_2) is sensitive to the variation of Q, while I(S_2,S_3) is sensitive to the change of r. The physical reasons for these results are explored and discussed. Apart from these, I(S_1,S_2)remains its value above 1 under the condition in this paper, but on the contrary, I(S_2, S_3) keeps its value well below 1. It proves that S2 and S_3 of Stokes vectors are inseparable from each other, thus output signals E_a and E_b of our scheme exhibit bipartite entanglement. The best entanglement appears nearly at about 70 MHz, at this point the minimum I(S_2, S_3) value is 0.25.
As a widely utilized information carrier, polarization microwave shows plenty of merits. Quantum microwave is booming gradually due to the development of superconducting technology, which makes it a promising potential to apply quantum entanglement to polarization microwave. In this paper, we introduce the concept of continuous variable polarization entanglement. Meanwhile, a scheme of polarization entanglement in microwave domain is proposed and simulated. The detail derivations are given and discussed. Polarization entangled microwaves are prepared by combining quadrature entangled signals and strong coherent signals on polarization beam splitters, and quadrature entangled signals are prepared by utilizing Josephson mixer. In order to probe the polarization entanglement between output signals, inseparability of Stokes vectors I(S_1,S_2)and I(S_2,S_3),is analyzed in 100 MHz operation bandwidth of Josephson mixer. The relation between inseparability I and squeezing degree r and between inseparability I and amplitude ratio Q are analyzed respectively. The results show that I(S_1,S_2) is sensitive to the variation of Q, while I(S_2,S_3) is sensitive to the change of r. The physical reasons for these results are explored and discussed. Apart from these, I(S_1,S_2)remains its value above 1 under the condition in this paper, but on the contrary, I(S_2, S_3) keeps its value well below 1. It proves that S2 and S_3 of Stokes vectors are inseparable from each other, thus output signals E_a and E_b of our scheme exhibit bipartite entanglement. The best entanglement appears nearly at about 70 MHz, at this point the minimum I(S_2, S_3) value is 0.25.
引文
[1] Einstein A, Podolsky B, Rosen N 1935 Phys. Rev. 47 777
[2] Liu C C, Wang D, Sun W Y, Ye L 2017 Quantum Inf.Process. 16 219
[3] Ourjoumtsev A 2010 Nat. Photon. 4 136
[4] Bowen W P, Treps N, Schnabel R, Ralph T C, Lam P K2003 J. Opt. B:Quantum Semiclassical Opt. 5 s467
[5] Zhou L, Ou-Yang Y, Wang L, Sheng Y B 2017 Quantum Inf.Process. 16 151
[6] Bowen W P, Treps N, Schnabel R, Lam P K 2002 Phys. Rev.Lett. 89 253601
[7] Korolkova N, Leuchs G, Loudon R, Ralph T C, Silberhorn C2002 Phys. Rev. A 65 052306
[8] Guo J, Cai C X, Ma L, Liu K, Sun H X, Gao J R 2017 Sci.Rep. 7 4434
[9] Wu L, Liu Y H, Deng R J, Yan Z H, Jia X J 2017 Acta Opt.Sin. 5 0527001(in Chinese)[吴量,刘艳红,邓瑞婕,闫智辉,贾晓军2017光学学报5 0527001]
[10] Wu L, Yan Z H, Liu Y H, Deng R J, Jia X J, Xie C D, Peng K C 2016 Appl. Phys. Lett. 108 161102
[11] Zhou Y Y, Yu J, Yan Z H, Jia X J 2018 Acta Opt. Sin. 70727001(in Chinese)[周瑶瑶,蔚娟,闫智辉,贾晓军2018光学学报7 0727001]
[12] Chen Y F, Hover D, Sendelbach S, Maurer L N 2011 Phys.Rev. Lett. 107 217401
[13] Hofheinz M, Huard B, Portier F 2016 C. R. Phys. 17 679
[14] Flurin E, Roch N, Mallet F, Devoret M H, Huard B 2012Phys. Rev. Lett. 109 183901
[15] Roch N, Flurin E, Nguyen F, Morfin P, Campagne-Ibarcq P,Devoret M H, Huard B 2012 Phys. Rev. Lett. 108 147701
[16] Flurin E, Roch N, Pillet J D, Mallet F, Huard B 2015 Phys.Rev. Lett. 114 090503
[17] Robson B A 1974 The Theory of Polarization Phenomena(Oxford:Clarendon)
[18] Christopher S R 1998 Radio Sci. 33 1617
[19] Duan L M, Giedke G, Cirac J I, Zoller P 2000 Phys. Rev.Lett. 84 2722
[20] Flurin E 2014 Ph. D. Dissertation(Berkeley:University of California)
[21] Sneep J G, Verhoeven C J M 1990 IEEE J. Solid-State Circuits 25 692
[2] Liu C C, Wang D, Sun W Y, Ye L 2017 Quantum Inf.Process. 16 219
[3] Ourjoumtsev A 2010 Nat. Photon. 4 136
[4] Bowen W P, Treps N, Schnabel R, Ralph T C, Lam P K2003 J. Opt. B:Quantum Semiclassical Opt. 5 s467
[5] Zhou L, Ou-Yang Y, Wang L, Sheng Y B 2017 Quantum Inf.Process. 16 151
[6] Bowen W P, Treps N, Schnabel R, Lam P K 2002 Phys. Rev.Lett. 89 253601
[7] Korolkova N, Leuchs G, Loudon R, Ralph T C, Silberhorn C2002 Phys. Rev. A 65 052306
[8] Guo J, Cai C X, Ma L, Liu K, Sun H X, Gao J R 2017 Sci.Rep. 7 4434
[9] Wu L, Liu Y H, Deng R J, Yan Z H, Jia X J 2017 Acta Opt.Sin. 5 0527001(in Chinese)[吴量,刘艳红,邓瑞婕,闫智辉,贾晓军2017光学学报5 0527001]
[10] Wu L, Yan Z H, Liu Y H, Deng R J, Jia X J, Xie C D, Peng K C 2016 Appl. Phys. Lett. 108 161102
[11] Zhou Y Y, Yu J, Yan Z H, Jia X J 2018 Acta Opt. Sin. 70727001(in Chinese)[周瑶瑶,蔚娟,闫智辉,贾晓军2018光学学报7 0727001]
[12] Chen Y F, Hover D, Sendelbach S, Maurer L N 2011 Phys.Rev. Lett. 107 217401
[13] Hofheinz M, Huard B, Portier F 2016 C. R. Phys. 17 679
[14] Flurin E, Roch N, Mallet F, Devoret M H, Huard B 2012Phys. Rev. Lett. 109 183901
[15] Roch N, Flurin E, Nguyen F, Morfin P, Campagne-Ibarcq P,Devoret M H, Huard B 2012 Phys. Rev. Lett. 108 147701
[16] Flurin E, Roch N, Pillet J D, Mallet F, Huard B 2015 Phys.Rev. Lett. 114 090503
[17] Robson B A 1974 The Theory of Polarization Phenomena(Oxford:Clarendon)
[18] Christopher S R 1998 Radio Sci. 33 1617
[19] Duan L M, Giedke G, Cirac J I, Zoller P 2000 Phys. Rev.Lett. 84 2722
[20] Flurin E 2014 Ph. D. Dissertation(Berkeley:University of California)
[21] Sneep J G, Verhoeven C J M 1990 IEEE J. Solid-State Circuits 25 692