数-相量子化及介观电路在自由热态下的量子效应

J4 ›› 2009, Vol. 26 ›› Issue (3): 333-337.

数-相量子化及介观电路在自由热态下的量子效应

王帅

菏泽学院物理系, 山东菏泽274015

收稿日期:2008-05-14 修回日期:2008-06-02 出版日期:2009-05-28 发布日期:2009-05-07
通讯作者: 王帅(1979－),男,山东平邑人,菏泽学院物理系讲师,硕士,主要从事电动力学的教学和量子光学的研究工作. E-mail:wangshuai197903@sohu.com
基金资助:
菏泽学院自然科学基金资助项目(XY07WL01)

Number-phase quantization and the quantum effects of mesoscopic circuit in free thermal state

WANG Shuai

Department Physics of Heze College, Shandong Heze, 274015

Received:2008-05-14 Revised:2008-06-02 Published:2009-05-28 Online:2009-05-07

摘要/Abstract

摘要：

利用数-相量子化方案，将介观LC电路等效为一个谐振子. 通过相干态表象和算符正规乘积形式,简捷的给出了自由热态的Wigner函数,同时借助于量子算符及其Weyl-Wigner对应研究了体系中电荷数及相位差在自由热态下的量子效应. 结果表明, 体系中电荷数及相位差在自由热态下的量子涨落不仅和电路中器件的参数有关,而且还和温度有关,且储存于电感中的平均能量和电容中的平均能量分别相等. 这一研究结果支持了介观电路数-相量子化新方案,对介观电路的量子化和电路的量子效应的研究具有很好的理论指导意义.

关键词: 量子光学, 介观LC电路, 数-相量子化, Wigner函数, 量子涨落

Abstract:

Using Number-phase quantization scheme, mesoscopic LC circuit is quantized to one dimensional harmonic oscillator coupled to a thermal field. The Wigner function of the free thermal state is obtained by using the coherent state representation and normal product form of operators, and then, the quantum effects of charge number and phase-difference in free thermal state are discussed by using Weyl-Wigner correspondence. It is found that, the quantum fluctuations of charge number and phase-difference in free thermal state are related not only the parameters of the circuit, but also the temperature, and the average energy stored in the capacitance and inductance is equal to each other. It is proven that the number-phase quantization is very useful to tackle with quantization of some mesoscopic circuits and the quantum effects.

Key words: quantum optics, mesoscopic LC circuit, number-phase quantization, Wigner function, quantum fluctuation

中图分类号:

O431.2

王帅 . 数-相量子化及介观电路在自由热态下的量子效应[J]. J4, 2009, 26(3): 333-337.

WANG Shuai . Number-phase quantization and the quantum effects of mesoscopic circuit in free thermal state[J]. J4, 2009, 26(3): 333-337.

参考文献

[1] Louisell W H. Quantum Statistical Properties of Radiation [M]. New York: John Wiley, 1973, Chapter 4.
[2] Wang Jisuo, Liu Tangkun, Zhan Mingsheng. Quantum fluctuations of a mesoscopic capacitance coupling circuits in a displaced squeezed Fock state [J]. Acta Physica Sinica.(物理学报),2000,49(11):2271-2275(in Chinese).
[3] Xu Xinglei, Li Hongqi, Wang Jisuo.The quantum fluctuation of mesoscopic damped mutual capacitance coupled double resonance RLC circuit in excitation state of the squeezed vacuum state [J]. International Journal of Theoretical Physics,2006,45(12):2231-2562.
[4] Liang Baolong, Li yanling, Meng xiangguo,et al. Quantization of mesoscopic RLC circuit and its quantum effects at finite temperature [J]. Chinese Journal of Quantum Electronics(量子电子学报),2007,24(3):335-340(in Chinese).
[5] Xu Xinglei, Li Hongqi, Wang Jisuo. Quantum fluctuation of mesoscopic RLC circuit involving complicated in thermal squeezed state [J].Physica B,2007,396(1-2):199-206.
[6] Fan Hongyi, Yue Fan, Song Tongqiang. Quantum theory of mesoscopic electric circuits in entangled state representation [J]. Phys.Lett.A,2002,305(5):222-230.
[7] Fan Hongyi, Wang Jisuo, Tang Xubing, et al. Number-phase quantization scheme for LC circuit and Josephson junction's Cooper pairs [J]. Chinese Journal of Quantum Electronics(量子电子学报),2007,24(2):168-172(in Chinese).
[8] Meng Xiangguo, Wang Jisuo, Zhai Yun,et al. Number-phase quantization and deriving energy-Level gap of two LC circuits with mutual-inductance [J].Chin.Phys.Lett.,2008.25(4):1025-1028.
[9] Department of Physics, Peking University. Quantum Statistical Physics [M]. Beijing: Peking University Press, 1987, P28-55(in Chinese).
[10] Qu Licheng, Wu Yuxi, He Qiliang. Quantum fluctuations of mesoscopic LC circuit at finite temperature [J]. Chinese Journal of Quantum Electronics(量子电子学报), 2006,23(6):0848-0852(in Chinese).
[11] Fan Hongyi. Entangled State Representations in Quantum Mechanics and Their Application [M]. Shanghai:Shanghai Scientific & Technical Publishers,1997,167-170 (in Chinese).
[12] Fan Hongyi. Application of Weyl-Wigner method in calculating thermal averages [J]. Commun Theor Phys, 1991, 16(1):123 -128.
[13] Fan Hongyi, Liang Xianting. Quantum fluctuation in thermal vaccuum state for mesoscopic LC electric circuit [J]. Chin.Phys.Lett., 2000,17(3) : 174-176.
[14] Liang Baolong, Wang Jisuo, Fan Hongyi. Marginal distributions of Wigner function in a mesoscopic LC circuit at finite temperature and the thermal Wigner operator [J]. International Journal of Theoretical Physics, 2007,46(7): 1779-1785.

[1]	陈骊颖, 黄堃, 王琪, 闫仕农 . 基于金刚石NV色心集成振动检测模块的设计[J]. 量子电子学报, 2023, 40(4): 500-509.
[2]	摆海龙, 白金海, 胡栋, 王宇. 用于原子干涉重力仪的小型频率合成器设计与实现[J]. 量子电子学报, 2023, 40(4): 510-518.
[3]	李嵩松. 玻色-爱因斯坦凝聚体中三体和四体相互作用对自旋压缩和量子纠缠的影响研究[J]. 量子电子学报, 2023, 40(4): 519-527.
[4]	李艳, . 一维强相互作用的玻色-费米混合气体关联特性研究[J]. 量子电子学报, 2023, 40(4): 528-540.
[5]	王晟, 方晓明, 林昱, 张天兵, 冯宝, 余杨, 王乐 . 四强度诱骗态相位匹配量子密钥分发协议[J]. 量子电子学报, 2023, 40(4): 541-545.
[6]	孙一石, 孙弋 . 基于BP 神经网络的经典-量子信号共纤同传系统参数预测[J]. 量子电子学报, 2023, 40(4): 546-559.
[7]	戚志明, 梁文耀 . 光束偏振对全息干涉制作复式光子晶体的影响研究[J]. 量子电子学报, 2023, 40(4): 447-457.
[8]	何业锋, 李丽娜∗, 白倩, 陈思昊, 强雨薇 . 标记单光子源下探测器死时间的量子密钥分配[J]. 量子电子学报, 2023, 40(1): 112-119.
[9]	谈志杰杨海瑞喻虹韩申生. X光强度关联衍射成像技术研究进展[J]. 量子电子学报, 2022, 39(6): 851-862.
[10]	林惠祖刘伟涛孙帅杜隆坤常宸李月刚. 关联成像算法研究进展[J]. 量子电子学报, 2022, 39(6): 863-879.
[11]	王孝艳, 王志远, 陈子阳, 蒲继雄∗. 基于深度学习技术从散斑场中识别多涡旋结构的轨道角动量[J]. 量子电子学报, 2022, 39(6): 955-961.
[12]	李能菲孙宇松黄见. 余弦编码复用高空间分辨率关联成像研究[J]. 量子电子学报, 2022, 39(6): 973-982.
[13]	戴攀, 庞志广, 李剑, 王琴∗. 基于纠缠源的非线性贝尔不等式研究[J]. 量子电子学报, 2022, 39(5): 761-767.
[14]	周贤韬, 江英华∗, 郭晨飞, 赵宁, 刘彪. 基于 GHZ 态粒子和单光子混合的量子安全直接通信协议[J]. 量子电子学报, 2022, 39(5): 768-775.
[15]	李天秀, 石磊∗, 王俊辉, 李佳豪. 基于深度学习的量子信号大气衰减系数预测[J]. 量子电子学报, 2022, 39(5): 786-794.