正负电子湮灭生成可控光子纠缠的研究
|
摘要
量子纠缠态是指多粒子体系不能写成单个粒子态的直积形式的物理状态，它具有的非局域性和测量斩断关联性的特征在量子信息科学里潜在广阔的应用前景。人们利用光学非线性特性在实验室上已获得多个光子在两个偏振方向上的纠缠态，而利用QED中腔场与原子的共振原理也可实现多原子纠缠态的制备。另外，关于利用离子在量子阱中制备离子的纠缠态也有了相关的报导。通常，获得粒子之间量子纠缠的形式都是以非相对论极限为理论前提，以光与原子的相互作用为理论基础，而所有光与原子相互作用的力现象均属于四大基本作用力中的电磁相互作用力。众所周知，光子是具有相对论性的麦克斯韦方程组二次量子化的产物，电子自旋和电子内禀磁矩原则上也是相对论效应的产物，Dirac方程的二次量子化形式是描述多电子性质的运动学方程。光子和电子又是一切微观量子现象的理论模型，因此深入研究相对论情形下的量子纠缠和量子关联是有意义的。
在非相对论情况下，光子是在原子能级之间激发跃迁而辐射出来的，而按照玻尔兹曼的统计规律，粒子的分布总是处于最低的能级状态，只有少量能激发到高能级状态，所以从这个意义上讲人们是无法获得高能光子之间的纠缠现象。本文将主要从量子场理论出发，结合量子态的叠加原理和自旋为1/2粒子的量子纠缠形式,探讨初始状态处于Bell型态的正负电子对发生湮灭生成光子的纠缠形式。
论文的内容分为五个部分，具体的安排为：第一章为研究背景，简介量子理论的发展概况和量子纠缠的性质以及它在未来量子信息和量子通信当中潜在的应用，同时也将介绍量子通信存在的若干问题；第二章为电磁不变性理论，主要涉及规范变换不变性和相对论洛仑兹变换不变性，着重介绍AB效应在本文中控制正负电子对初态的可能性；第三章为量子场论的基本原理，该部分内容将重点介绍在电磁相互作用下存在各种守恒量的前提条件，如能量动量守恒和角动量守恒，宇称守恒，以及电荷守恒的各种依据；第四章为纠缠正负电子对的湮灭，这是本论文的中心内容，重点讲述在三级玻恩近似下正负电子对湮灭生成光子末态的具体形式；最后给出总结和展望，高能光子受干扰程度小，穿透力强，高能光子关联可以运用到物体内部的三维成像并有一定的潜在价值，同时它将架起量子纠缠非局域性和爱因斯坦狭义相对论定域实在论的桥梁，为区别在原子与腔场之间纠缠的转移，在未来研究纠缠转化和守恒的问题上将具有重大的而且现实的物理意义。
The state of Quantum Entanglement is defined by that the state of multi-particles’system can be not written as a form of product of single-particle state. Its non-localproperty and the sudden-broken character of quantum correlation after measuring inquantum state exist a wide used prospect in quantum information science. Peoplehave obtained quantum entangled state of multi-photons in two polarizationorientation in experiment by non-linearity of optics, while the preparation ofmulti-atoms’ entangled state were realized in QED by used the resonance principle. Inaddition, there are relevant reports about making ion entangled state in quantum trap.Generally, attaining the form of quantum entanglement between particles is premisedin theory by the limitation of non-relativity theory and is basic by the interaction ofphoton and electron. But all the force phenomenons within the interaction of photonand atom belong to the force of electromagnetic interaction which one of the fourfundamental forces. However, as is well known that photon is the outcome of thesecond quantification of the Maxwell’s equation group, and electron spin and themagnetic moment of electron are also the results from an effect of relativity.Furthermore, the form of second quantification of the Dirac equation is a motionequation that describes the property of electrons. Photon and electron are the theorymodel of all the microcosmic quantum phenomenon. Therefore, it is significant to gointo doing more research in quantum entanglement and cuantum correlation.
Under this circumstance of non-relativity, photon gives out from the transitionbetween two energy levels at the inner of an atom. According to the rule of Boltzmannstatistics, the distribution of particles is always at the lowest state of the energy leveland only a few can stimulate to higher states. So from this mean people are not able togain an entangled state among high-energy photons. In this paper, beginning with thetheory of quantum field and combining the superposition principle of quantum stateand the entangled forms of spin-1/2particles, we will discuss the photons’ entangledstate which is generated from the annihilation of positron-electron pair, and here thepositron-electron pair is in Bell-like state of its initial state. The content of paper willbe divided into five sections, the specific arrange are as follow:
The first chapter is the background of this research; it takes a brief introductionabout the general situation of the development of quantum theory and the nature ofquantum entanglement with its potential use in future quantum information andquantum communication. Meanwhile it is going to introduce some existing problemsin quantum communication. The second chapter is the theory of electromagneticinvariance property. It mainly refers to the invariance of the norm conversion and theinvariance of Lorentz conversion under the theory of relativity. It emphatically takesan account about the importance in controlling the initial state of positron-electronpair possibly by using AB effect. The third chapter is the elementary principle ofquantum theory. The content of this part will emphasis to introduce the premisecondition for all kinds of conservation under the electromagnetic interaction. Such askinds of judging about the conservation of energy and momentum and circularmomentum, the conservation of parity, and the conservation of electric charge.Chapter four is the annihilation of entangled positron-electron pair. This is the main content in the paper. Here I stress to represent specific form of the photons’ final statewhich is generated from the annihilation of the particles pair within three-Bornapproximation. Finally, we give the conclusion and the expectation. High energyphotons have a low disturbance and have a high penetrating. The correlation of highenergy photons can be use in three-dimensional imaging of objects and has a certainpotential value. At the same time it frames a bridge between non-locality of quantumentanglement and local realism of Einstein’s special theory of relativity. In order todistinguish the entanglement transfer between atoms and cavity field, taking a deeperresearch in entanglement transform and entanglement conversation in the future willbe very important and realistic in physics.
在非相对论情况下，光子是在原子能级之间激发跃迁而辐射出来的，而按照玻尔兹曼的统计规律，粒子的分布总是处于最低的能级状态，只有少量能激发到高能级状态，所以从这个意义上讲人们是无法获得高能光子之间的纠缠现象。本文将主要从量子场理论出发，结合量子态的叠加原理和自旋为1/2粒子的量子纠缠形式,探讨初始状态处于Bell型态的正负电子对发生湮灭生成光子的纠缠形式。
论文的内容分为五个部分，具体的安排为：第一章为研究背景，简介量子理论的发展概况和量子纠缠的性质以及它在未来量子信息和量子通信当中潜在的应用，同时也将介绍量子通信存在的若干问题；第二章为电磁不变性理论，主要涉及规范变换不变性和相对论洛仑兹变换不变性，着重介绍AB效应在本文中控制正负电子对初态的可能性；第三章为量子场论的基本原理，该部分内容将重点介绍在电磁相互作用下存在各种守恒量的前提条件，如能量动量守恒和角动量守恒，宇称守恒，以及电荷守恒的各种依据；第四章为纠缠正负电子对的湮灭，这是本论文的中心内容，重点讲述在三级玻恩近似下正负电子对湮灭生成光子末态的具体形式；最后给出总结和展望，高能光子受干扰程度小，穿透力强，高能光子关联可以运用到物体内部的三维成像并有一定的潜在价值，同时它将架起量子纠缠非局域性和爱因斯坦狭义相对论定域实在论的桥梁，为区别在原子与腔场之间纠缠的转移，在未来研究纠缠转化和守恒的问题上将具有重大的而且现实的物理意义。
The state of Quantum Entanglement is defined by that the state of multi-particles’system can be not written as a form of product of single-particle state. Its non-localproperty and the sudden-broken character of quantum correlation after measuring inquantum state exist a wide used prospect in quantum information science. Peoplehave obtained quantum entangled state of multi-photons in two polarizationorientation in experiment by non-linearity of optics, while the preparation ofmulti-atoms’ entangled state were realized in QED by used the resonance principle. Inaddition, there are relevant reports about making ion entangled state in quantum trap.Generally, attaining the form of quantum entanglement between particles is premisedin theory by the limitation of non-relativity theory and is basic by the interaction ofphoton and electron. But all the force phenomenons within the interaction of photonand atom belong to the force of electromagnetic interaction which one of the fourfundamental forces. However, as is well known that photon is the outcome of thesecond quantification of the Maxwell’s equation group, and electron spin and themagnetic moment of electron are also the results from an effect of relativity.Furthermore, the form of second quantification of the Dirac equation is a motionequation that describes the property of electrons. Photon and electron are the theorymodel of all the microcosmic quantum phenomenon. Therefore, it is significant to gointo doing more research in quantum entanglement and cuantum correlation.
Under this circumstance of non-relativity, photon gives out from the transitionbetween two energy levels at the inner of an atom. According to the rule of Boltzmannstatistics, the distribution of particles is always at the lowest state of the energy leveland only a few can stimulate to higher states. So from this mean people are not able togain an entangled state among high-energy photons. In this paper, beginning with thetheory of quantum field and combining the superposition principle of quantum stateand the entangled forms of spin-1/2particles, we will discuss the photons’ entangledstate which is generated from the annihilation of positron-electron pair, and here thepositron-electron pair is in Bell-like state of its initial state. The content of paper willbe divided into five sections, the specific arrange are as follow:
The first chapter is the background of this research; it takes a brief introductionabout the general situation of the development of quantum theory and the nature ofquantum entanglement with its potential use in future quantum information andquantum communication. Meanwhile it is going to introduce some existing problemsin quantum communication. The second chapter is the theory of electromagneticinvariance property. It mainly refers to the invariance of the norm conversion and theinvariance of Lorentz conversion under the theory of relativity. It emphatically takesan account about the importance in controlling the initial state of positron-electronpair possibly by using AB effect. The third chapter is the elementary principle ofquantum theory. The content of this part will emphasis to introduce the premisecondition for all kinds of conservation under the electromagnetic interaction. Such askinds of judging about the conservation of energy and momentum and circularmomentum, the conservation of parity, and the conservation of electric charge.Chapter four is the annihilation of entangled positron-electron pair. This is the main content in the paper. Here I stress to represent specific form of the photons’ final statewhich is generated from the annihilation of the particles pair within three-Bornapproximation. Finally, we give the conclusion and the expectation. High energyphotons have a low disturbance and have a high penetrating. The correlation of highenergy photons can be use in three-dimensional imaging of objects and has a certainpotential value. At the same time it frames a bridge between non-locality of quantumentanglement and local realism of Einstein’s special theory of relativity. In order todistinguish the entanglement transfer between atoms and cavity field, taking a deeperresearch in entanglement transform and entanglement conversation in the future willbe very important and realistic in physics.
引文
[1] S.N.Gupta,[J],Phys.Rev.107,1722(1957).
[2] S.N.Gupta, Canad,[J],J.Phys.35,901(1957).
[3] S.N.Gupta,[J],Proc.Phys.Soc.London A63,681(1950).
[4]邹兴国著.量子场论导论[M]科学出版社,P38.
[5] A. Einstein B. Podolsky and N. Rosen, Can quantum mechanicaldesription of physical reality be considered compete?[J]. Phys. Rev.,47(1935),777.
[6] E. Schro&&dinger, Naturwissenschaften23(1935),807-812,823-828,844-849, Die gegenwa&&rtige Situation in der Quantenmechanik[J].
[7] J.Bell,Physics，1（1964）195，“On the Einstein-Podolsky-Rosen Paradox.”[J]
[8] J.F. Clauser, M.A. Horne, A.Shimony and R.A. Holt.“ProposedExperiment to Test Local-Hidden-Variable Theories.”[J].Phys. Rev.lett.,23(1969),880.
[9]徐在新著.高等量子力学[M]华东师范大学出版社,P36-49.
[10]曾谨言著.量子力学导论[M]第二版,北京大学出版社,P319-320.
[11]邹兴国著.量子场论导论[M]科学出版社,P86-87.
[12]邹兴国著.量子场论导论[M]科学出版社,P90.
[13] Zhongxiao Man, Yingjie Zhang and Yunjie Xia. Entanglement dynamicsof multqubit system in Markovian and non-Markovian reserviors[J].European physical Journal D,2010,58:147-151.
[14] Zhongxiao Man, Yunjie Xia and Nguyen Ba An. Entanglement dynamicsof W-like states within the framework of triple Jaynes Cummingsmodel. Journal of Modern Optics[J],2009,56:1022-1028.
[15] M. Planck, Ann. Der Physik,[J],4(1901),553.
[16] A. Einstein, Ann. Der Physik,[J],17(1905),132.
[17]郭硕鸿著.电动力学[M]第二版,高等教育出版社,P266.
[18]郭硕鸿著.电动力学[M]第二版,高等教育出版社,P261.
[19]邹兴国著.量子场论导论[M]科学出版社,P28.
[20]邹兴国著.量子场论导论[M]科学出版社,P29.
[21]邹兴国著.量子场论导论[M]科学出版社,P33.
[22]邹兴国著.量子场论导论[M]科学出版社,P32.
[23]邹兴国著.量子场论导论[M]科学出版社,P41.
[24] Quantum Electrodynamics[M], Suraj, N. Gupta, Gordon and BreachScience Publishers,1977,P10.
[25] Y. Aharonov and D. Bohm,[J], Phys. Rev.115(1959)485.
[26]曾谨言著.量子力学导论[M]第二版,北京大学出版社P205.
[27]曾谨言著.量子力学[M]卷Ⅱ,第四版,科学出版社P386.
[28]曾谨言著.量子力学[M]卷Ⅱ,第四版,科学出版社P390.
[29]邹兴国著.量子场论导论[M]科学出版社P45.
[30]邹兴国著.量子场论导论[M]科学出版社P58-60.
[31]邹兴国著.量子场论导论[M]科学出版社P66.
[32] A. Acin, J.I.Latorre, and P.Pascual. Three-party entanglement frompositronium[J]. Phys. Rev. A.,63,042107(2001).
[33] Quantum Electrodynamics[M], Suraj, N. Gupta, Gordon and BreachScience Publishers,1977,P140.
[34] Quantum Electrodynamics[M], Suraj, N. Gupta, Gordon and BreachScience Publishers,1977,P84-85.
[35]唐孝威，正负电子三光子湮没实验研究[J]，中国科学，A辑，第七期.
[36] Mahdi Hosseini,Ben M.Sparkes et al. Coherent optical pulse sequencerfor quantum applications[J]. Nature,461,08325(2009).
[37] Honda,K.et al.Storage and retrievalof a squeezed vacuum[J]. Phys.Rev. lett.,100,093601(2008).
[38] Appel,J.Figueroa,E.orystov,D.Lobino,M.&Lvovsky,A.L.Quantum memoryfor squeeze light. Phys. Rev. lett.,100,093602(2008).
[39]Hetet,G.Longdell,J.J.,Alexander,A.L.,Lam,P.K.&Sellars,M.J.Electro-optic quantum memory for light using two-level atoms. Phys. Rev.lett.,100,023601(2008).
[40] Gorshkov,A.V.,Andre,A.,Lukin,M.D.&Sorensen,A.S.Photon storge inΛ-type optically dense atomic media.I.Cavity model[J]. Phys. Rev. A.,76,033804(2007).
[41] Simon,C.et al.Quantum repeaters with photon pair sources andmultimode memories[J]. Phys. Rev. lett.,98,190503(2007).
[42] Brendel,J.,Gisin,N.,Tittel,W.&Zbinden,H.Pulsed energy-timeentangled twin-photon source for quantum communication[J]. Phys. Rev.lett.,82,2594-2597(1999).
[43] Fleischhauer,M.&Lukin, M.D.Dark-state polaritons inelectromagnetically induced transparency[J]. Phys. Rev. lett.,84,5094-5097(2000).
[44] Eisaman,M.D.et al. Electromagnetically induced transparency withtunable single-photon pulses[J].Nuture438,837-841(2005).
[45] Cirac J,Zoller P.Preparation of macroscopic superpositions in manyatom systems[J]. Phys. Rev. A.,1994,50(4):R2799-R2802.
[46] Hagley E, Maitre X, Nogues G,et al. Generation ofEinstein-Podolsky-Rosen pairs of atoms[J]. Phys. Rev. Lett.,1997,79(1):1-5
[2] S.N.Gupta, Canad,[J],J.Phys.35,901(1957).
[3] S.N.Gupta,[J],Proc.Phys.Soc.London A63,681(1950).
[4]邹兴国著.量子场论导论[M]科学出版社,P38.
[5] A. Einstein B. Podolsky and N. Rosen, Can quantum mechanicaldesription of physical reality be considered compete?[J]. Phys. Rev.,47(1935),777.
[6] E. Schro&&dinger, Naturwissenschaften23(1935),807-812,823-828,844-849, Die gegenwa&&rtige Situation in der Quantenmechanik[J].
[7] J.Bell,Physics，1（1964）195，“On the Einstein-Podolsky-Rosen Paradox.”[J]
[8] J.F. Clauser, M.A. Horne, A.Shimony and R.A. Holt.“ProposedExperiment to Test Local-Hidden-Variable Theories.”[J].Phys. Rev.lett.,23(1969),880.
[9]徐在新著.高等量子力学[M]华东师范大学出版社,P36-49.
[10]曾谨言著.量子力学导论[M]第二版,北京大学出版社,P319-320.
[11]邹兴国著.量子场论导论[M]科学出版社,P86-87.
[12]邹兴国著.量子场论导论[M]科学出版社,P90.
[13] Zhongxiao Man, Yingjie Zhang and Yunjie Xia. Entanglement dynamicsof multqubit system in Markovian and non-Markovian reserviors[J].European physical Journal D,2010,58:147-151.
[14] Zhongxiao Man, Yunjie Xia and Nguyen Ba An. Entanglement dynamicsof W-like states within the framework of triple Jaynes Cummingsmodel. Journal of Modern Optics[J],2009,56:1022-1028.
[15] M. Planck, Ann. Der Physik,[J],4(1901),553.
[16] A. Einstein, Ann. Der Physik,[J],17(1905),132.
[17]郭硕鸿著.电动力学[M]第二版,高等教育出版社,P266.
[18]郭硕鸿著.电动力学[M]第二版,高等教育出版社,P261.
[19]邹兴国著.量子场论导论[M]科学出版社,P28.
[20]邹兴国著.量子场论导论[M]科学出版社,P29.
[21]邹兴国著.量子场论导论[M]科学出版社,P33.
[22]邹兴国著.量子场论导论[M]科学出版社,P32.
[23]邹兴国著.量子场论导论[M]科学出版社,P41.
[24] Quantum Electrodynamics[M], Suraj, N. Gupta, Gordon and BreachScience Publishers,1977,P10.
[25] Y. Aharonov and D. Bohm,[J], Phys. Rev.115(1959)485.
[26]曾谨言著.量子力学导论[M]第二版,北京大学出版社P205.
[27]曾谨言著.量子力学[M]卷Ⅱ,第四版,科学出版社P386.
[28]曾谨言著.量子力学[M]卷Ⅱ,第四版,科学出版社P390.
[29]邹兴国著.量子场论导论[M]科学出版社P45.
[30]邹兴国著.量子场论导论[M]科学出版社P58-60.
[31]邹兴国著.量子场论导论[M]科学出版社P66.
[32] A. Acin, J.I.Latorre, and P.Pascual. Three-party entanglement frompositronium[J]. Phys. Rev. A.,63,042107(2001).
[33] Quantum Electrodynamics[M], Suraj, N. Gupta, Gordon and BreachScience Publishers,1977,P140.
[34] Quantum Electrodynamics[M], Suraj, N. Gupta, Gordon and BreachScience Publishers,1977,P84-85.
[35]唐孝威，正负电子三光子湮没实验研究[J]，中国科学，A辑，第七期.
[36] Mahdi Hosseini,Ben M.Sparkes et al. Coherent optical pulse sequencerfor quantum applications[J]. Nature,461,08325(2009).
[37] Honda,K.et al.Storage and retrievalof a squeezed vacuum[J]. Phys.Rev. lett.,100,093601(2008).
[38] Appel,J.Figueroa,E.orystov,D.Lobino,M.&Lvovsky,A.L.Quantum memoryfor squeeze light. Phys. Rev. lett.,100,093602(2008).
[39]Hetet,G.Longdell,J.J.,Alexander,A.L.,Lam,P.K.&Sellars,M.J.Electro-optic quantum memory for light using two-level atoms. Phys. Rev.lett.,100,023601(2008).
[40] Gorshkov,A.V.,Andre,A.,Lukin,M.D.&Sorensen,A.S.Photon storge inΛ-type optically dense atomic media.I.Cavity model[J]. Phys. Rev. A.,76,033804(2007).
[41] Simon,C.et al.Quantum repeaters with photon pair sources andmultimode memories[J]. Phys. Rev. lett.,98,190503(2007).
[42] Brendel,J.,Gisin,N.,Tittel,W.&Zbinden,H.Pulsed energy-timeentangled twin-photon source for quantum communication[J]. Phys. Rev.lett.,82,2594-2597(1999).
[43] Fleischhauer,M.&Lukin, M.D.Dark-state polaritons inelectromagnetically induced transparency[J]. Phys. Rev. lett.,84,5094-5097(2000).
[44] Eisaman,M.D.et al. Electromagnetically induced transparency withtunable single-photon pulses[J].Nuture438,837-841(2005).
[45] Cirac J,Zoller P.Preparation of macroscopic superpositions in manyatom systems[J]. Phys. Rev. A.,1994,50(4):R2799-R2802.
[46] Hagley E, Maitre X, Nogues G,et al. Generation ofEinstein-Podolsky-Rosen pairs of atoms[J]. Phys. Rev. Lett.,1997,79(1):1-5