用归一化的光子态矢函数描述孪生双光子思想实验
Description of Twin Two-Photon Thought Experiment with Normalized Photonic State-Vector Function
摘要: 根据Born对归一化波函数的概率解释,从量子力学的观点重新审视孪生双光子思想实验,着眼的对象不再是这对孪生光子本身,而是一群具有共同属性的光子集合。所有这些光子具有完全相同的能量和角动量特征,但是在动量的相反方向却具有相等的概率;或者说这是一群在相反动量方向具有相等的数量、而所有其它量子特征完全相同的光子集合。仿效先前对光学双孔效应进行量子力学分析的步骤,具体构造出描述孪生双光子思想实验总的归一化光子态矢函数,所描述的并不是两个光子之间的纠缠,而是单个光子的概率,从而得到光子的空间分布函数。当光子的总数达到形成完整图像的统计学要求时,宏观上将显示出明暗间隔的条纹。在追溯纠缠态历史渊源的基础上,返璞归真孪生双光子思想实验的量子力学观点,对所谓的EPR佯谬引发出来的双光子纠缠态作出了新的解释,提出了量子信息的新认识。 Based on Born’s statistical interpretation for the normalized wave function, the twin two-photon thought experiment is reexamined from point of view of quantum mechanics. The emphasis is no longer the pair of twin photons itself, but rather a group of photons with common attributes. All the photons have the characteristics of identical energy and angular momentum, but possess same probability in the opposite direction of momentum, that is to say, this is a group of photon collections, which have the same number in the opposite direction of momentum, while all other quantum characteristics are identical. Following the example of the previous procedure dealing with optical two-hole effect by use of quantum mechanics, the total normalized photonic state-vector function that described the twin two-photon thought experiment has been specifically constructed, which does not describe the entangled behavior of the two photons, but the probability of a single photon, and thus deduces the probability distribution of a photon in the space. When the total number of photons satisfies the statistical requirements to form a complete picture, some fringes of light and dark interval will be displayed. On the basis of retrospective historical origins of entanglement, the point of view of quantum mechanics about the twin two-photon thought experiment was reverted. The so-called EPR paradox, and the entangled two-photon state have been re-interpreted, and a new understanding of quantum information has been put forward.  
文章引用:姚志欣. 用归一化的光子态矢函数描述孪生双光子思想实验[J]. 应用物理, 2012, 2(4): 121-133. http://dx.doi.org/10.12677/APP.2012.24021

参考文献

[1] A. D. Aczel. Entanglement: The greatest mystery in physics. New York: Penguin Group (USA) Inc., 2001: XVI, 145, 235
[2] 周正威, 郭光灿. 量子纠缠态[J]. 物理, 2000, 29(11): 695- 699.
[3] 郭光灿. 量子信息科学在中国科学技术大学的兴起和发展[J]. 物理, 2008, 37(8): 556-561.
[4] 孙昌璞. 量子理论若干基本问题研究的新进展[J]. 物理学进展, 2001, 21(3): 317-360.
[5] 赵凯华, 罗蔚茵. 量子物理[M]. 北京: 高等教育出版社, 2001: 90.
[6] A. Einstein, B. Podolsky and N. Rosen. Can quantum-mechanical description of physical reality be considered complete? Physical Review, 1935, 47(10): 777-780.
[7] L. Mandel, E. Wolf. Optical coherence and quantum optics. Cambridge: Cambridge University Press, 1995: 649.
[8] W. A. Harrison. Applied quantum mechanics. Singapore: World Scientific, 2000: 10.
[9] 姚志欣, 潘佰良, 陈钢等. 光子的态矢量函数[J]. 物理学报, 2006, 55(5): 2158-2164.
[10] Z. X. Yao, J. W. Zhong and B. L. Pan. A complete description and applications for a photon. C. Roychoudhuri, Ed., Proceedings of SPIE Vol. 6664, Bellingham, SPIE, 2007, 6664OT1-9.
[11] R. Feynman. The character of physical law. Massachusetts: The M.I.T. Press, 1965: 130.
[12] D. Zu. The classical structure model of single photon and classical point of view with regard to wave-particle duality of photon. Progress in Electromagnetic Research Letters, 2008, 1: 109-118.
[13] Z. X. Yao, J. W. Zhong and B. L. Pan. Multi-pinhole optical interference and its quantum description. Optics Communications, 2011, 284(21): 5100-5104.
[14] 姚志欣, 钟建伟, 毛邦宁等. 双孔干涉效应的量子描述[J]. 物理学报, 2007, 56(6): 3185-3191.
[15] Z. X. Yao, J. W. Zhong, B. N. Mao, et al. Interference nature of light. Chinese Physics B, 2008, 17(2): 578-584.
[16] 喀兴林. 高等量子力学[M]. 北京: 高等教育出版社, 2001: 1.
[17] C. N. Yang. Thematic melodies of twentieth century theoretical physics: Quantization, symmetry and phase factor. International Journal of Modern Physics A, 2003, 18(19): 3263-3272.
[18] 姚志欣, 钟建伟, 潘佰良. 量子相位的公式表述和图像[J]. 中国科学G辑: 物理学•力学•天文学, 2009, 39(12): 1699- 1709.
[19] J. Gribbin. In search of Schrödinger’s cat. Toronto: Bantam Books, 1984: 194.
[20] M. O. Scully, M. S. Zubairy. Quantum optics. New York: Cambridge University Press, 1997: 9.
[21] M. Sara. Quantum mechanics. Oxford: Addison-Wesley Publishing Company Inc., 1993: 34.
[22] L. I. Schiff. Quantum mechanics (3rd Edition). New York: McGraw-Hill Book Company, 1968: 24-25.
[23] 关洪. 论爱因斯坦《关于光的产生和转化的一个试探性观点》一文的得失[J]. 自然辩证法通讯, 2005, 156(2): 7-11.
[24] P. A. M. Dirac. The principles of quantum mechanics (4th Edition). London: Oxford University Press, 1958: 9-10.
[25] P. L. Pfleegor, L. Mendel. Interference of independent photon beams. Physical Reviews, 1967, 159(5): 1084-1088.
[26] H. Paul. Interference of independent photons. Reviews of Modern Physics, 1986, 58(1): 209-231.
[27] R. J. Glauber. Dirac’s famous dictum on interference: One photon or two? American Journal of Physics, 1995, 63(1): 12.
[28] E. Hecht. Optics. San Francisco: Addison Wesley, 2002: 396.
[29] L. D. Laudau, E. M. Lifshitz. Quantum mechanics (non-relativistic theory) (3rd Edition). Oxford: Butterworth Heinemann, 1999: 51.
[30] J. S. Bell. On the problem of hidden variables in quantum me- chanics. Reviews of Modern Physics, 1966, 38(3): 447-452.
[31] J. S. Bell. On the Einstein podolsky rosen paradox. Physics, 1964, 1: 195-200.
[32] 韩跃清. 在量子信息学领域持续创新——访中国科学院院士、中国科技大学教授郭光灿[J]. 科技创新与品牌, 2009, 27: 11-13.