纠缠微波信号的特性及表示方法
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摘要
纠缠微波信号是电磁场微波频段量子特性的体现.在总结了现有纠缠微波信号产生及验证实验的基础上,针对目前没有统一的表达式来描述纠缠微波信号格式的问题,通过深入分析纠缠微波信号的特性,提出了两种纠缠微波信号的表示方法.一种是在量子框架下,利用双模压缩真空态表示,并分别在光子数表象下和Wigner分布下分析了其信号特征,刻画了正交分量之间的正反关联特性;另一种是在经典框架下,利用关联随机信号表示,刻画了测量后纠缠微波信号场幅度正交分量随时间变化的波形图.两种表示恰当合理地反映了纠缠微波信号连续变量纠缠的特性.
Entangled microwave signal is the reflection of the quantum characteristics of electromagnetic field in a GHz frequency range. Its generation is mainly dependent on superconducting circuits. Owing to the fact that there is no canonical expression to describe the format of entangled microwave signals, two expressional methods are presented on the basis of analyzing the characteristics of entangled microwave signals. One is in quantum frame, and the other is in classical frame. In quantum frame, we express entangled microwave signals in two-mode squeezed vacuum state.According to input-output relationship and parametric amplifier property in the generating process of entangled microwave signals, we describe the characteristics by two-mode squeezing operator and quantum Langevin equation. In the representation of photon number and Wigner function, we analyze the photon number distribution and the quadrature components' distribution of two-mode squeezed vacuum state, which shows the entangled two-photon correlation and the non-localized positive(negative) correlation of quadrature components. These are consistent with the characteristics of entangled microwave signals. Therefore, the results demonstrate that the entangled microwave signals can be expressed by two-mode squeezed vacuum state. In classical frame, we express entangled microwave signals in correlated random signals approximately. According to the relationship between quadrature components and the quantization of electromagnetic field, we construct the relation among electric-field intensity, input angular frequency, and squeezed parameter. The random number with Gaussian distribution is used as an input state to implement the simulation analysis. We illustrate the waveforms of entangled microwave signals after measurement and the extracted quadrature component waveform varying with time. The simulation results are consistent with the measurement results. These results show that the classical expression can reflect the one-path randomicity and two-path correlativity, which are the intrinsic characteristics of entangled microwave signals. Therefore, it is rational to express entangled microwave signals in correlated random signals. These two expressions properly reflect the continuous variable entanglement characteristics of entangled microwave signals. The expression of two-mode squeezed vacuum state is complete. Plenty of parameters that represent quantum information can be calculated by two-mode squeezed vacuum state, such as entanglement degree or the power of noise fluctuation. The merit of the expression of correlated random signals is intuitive, which makes it easier to understand the nonclassical characteristics of entangled microwave signals.
Entangled microwave signal is the reflection of the quantum characteristics of electromagnetic field in a GHz frequency range. Its generation is mainly dependent on superconducting circuits. Owing to the fact that there is no canonical expression to describe the format of entangled microwave signals, two expressional methods are presented on the basis of analyzing the characteristics of entangled microwave signals. One is in quantum frame, and the other is in classical frame. In quantum frame, we express entangled microwave signals in two-mode squeezed vacuum state.According to input-output relationship and parametric amplifier property in the generating process of entangled microwave signals, we describe the characteristics by two-mode squeezing operator and quantum Langevin equation. In the representation of photon number and Wigner function, we analyze the photon number distribution and the quadrature components' distribution of two-mode squeezed vacuum state, which shows the entangled two-photon correlation and the non-localized positive(negative) correlation of quadrature components. These are consistent with the characteristics of entangled microwave signals. Therefore, the results demonstrate that the entangled microwave signals can be expressed by two-mode squeezed vacuum state. In classical frame, we express entangled microwave signals in correlated random signals approximately. According to the relationship between quadrature components and the quantization of electromagnetic field, we construct the relation among electric-field intensity, input angular frequency, and squeezed parameter. The random number with Gaussian distribution is used as an input state to implement the simulation analysis. We illustrate the waveforms of entangled microwave signals after measurement and the extracted quadrature component waveform varying with time. The simulation results are consistent with the measurement results. These results show that the classical expression can reflect the one-path randomicity and two-path correlativity, which are the intrinsic characteristics of entangled microwave signals. Therefore, it is rational to express entangled microwave signals in correlated random signals. These two expressions properly reflect the continuous variable entanglement characteristics of entangled microwave signals. The expression of two-mode squeezed vacuum state is complete. Plenty of parameters that represent quantum information can be calculated by two-mode squeezed vacuum state, such as entanglement degree or the power of noise fluctuation. The merit of the expression of correlated random signals is intuitive, which makes it easier to understand the nonclassical characteristics of entangled microwave signals.
引文
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[24]Khrennikov A, Ohya M, Watanab N 2010 J. Russ. Laser Res. 31 462
[25]Bharath H M, Ravishankar V 2014 Phys. Rev. A 89062110
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[3]Braunstein S L, Loock P 2005 Rev. Mod. Phys. 77 513
[4]Gisin N, Thew R T 2010 Electro-n. Lett. 46 965
[5]Nielsea M A, Chuang I L 2000 Quantum Computation a-nd Quantum Information(New York:Cambridge University Press)
[6]Benjamin H 2016 G. R. Phys. 17 679
[7]Yamamoto T, Inomata K, Watanabe M, Matsuba K,Miyazaki T, Oliver W D, Nakamura Y, Tsai J S 2008Appl. Phys. Lett. 93 042510
[8]Zhong L, Menzel E P, Candia R D, Eder P, Ihmig M,Baust A, Haeberlein M, Hoffmann E, Inomata K, Yamamoto T, Nakamura Y, Solano E, Deppe F, Marx A,Gross R 2013 New J. Phys. 15 125013
[9]Eichler C, Bozyigit D, Lang C, Baur M, Steffen L, Fink J M, Filipp S, Vallraff A 2011 Phys.Rev. Lett. 107113601
[10]Menzel E P, Candia R D, Deppe F, Zhong L, Ihmig M,Haeberlein M, Baust A, Hoffmann E, Ballester D, Inomata K, Yamamoto T, Nakamura Y, Solano E, Marx A,Gross R 2012 Phys. Rev. Lett. 109 250502
[11]Flurin E, Roch N, Mallet F, Devoret M H, Huard B 2012Phys. Rev. Lett. 109 183901
[12]Dambach S, Kubala B, Ankerhold J 2017 New J. Phys.19 023027
[13]Mallet F, Castellanos-Beltran M A, Ku H S, Glancy S,Knill E, Irwin K D, Hilton G C, Vale L R, Lehnert K W2011 Phys. Rev. Lett. 106 220502
[14]Bergeal N, Schackert F, Metcalfe M, Vi.jay R,Manucharyan V E, Frunzio L, Prober D E, Schoelkopf R J, Girvin S M, Devoret M H 2010 Nature 465 64
[15]Abdo B, Kamal A, Devoret M H 2013 Phys. Rev. B 87014508
[16]Zhou X, Schmitt V, Bertet P, Vion D, Wustmann W,Shumeiko V, Esteve D 2014 Phys. Rev. B 89 214517
[17]Mutus J Y, White T C, Barends R, Chen Y, Chen Z,Chiaro B, Dunsworth A, Jeffrey E, Kelly J, Megrant A, Neill C, O'Malley P J J, Roushan P, Sank D,Vainsencher A, Wenner J, Sundqvist K M, Cleland A N, Martinis John M 2014 Appl. Phys. Lett. 104 263513
[18]Pillet J D, Flurin E, Mallet F, Huard B 2015 Appl. Phys.Lett. 106 083509
[19]Flurin E, Roch N, Pillet J D, Mallet F, Huard B 2015Phys. Rev. Lett. 114 090503
[20]Wu D W, Li X, Yang C Y, Miao Q 2017 Chin. J. Quantum Electron. 34 1(in Chinese)[吴德伟,李响,杨春燕,苗强2017量子电子学报34 1]
[21]Zhao Y J, Wang C Q, Zhu X B, Liu Y X 2016 Sci. Rep.6 23646
[22]Wang X L, Wu D W, Li X, Zhu H N, Chen K, Fang G2017 Acta Phys. Sin. 66 230302(in Chinese)[王湘林,吴德伟,李响,朱浩男,陈坤,方冠2017物理学报66 230302]
[23]Zhu H N, Wu D W, Li X, Wang X L, Miao Q, Fang G2018 Acta Phys. Sin. 67 040301(in Chinese)[朱浩男,吴德伟,李响,王湘林,苗强,方冠2018物理学报67 040301]
[24]Khrennikov A, Ohya M, Watanab N 2010 J. Russ. Laser Res. 31 462
[25]Bharath H M, Ravishankar V 2014 Phys. Rev. A 89062110