某些量子态和介观RLC电路的量子特性研究
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摘要
本论文报道了作者在攻读硕士学位期间的主要研究工作.在本学位论文中,我们研究了某些量子态和介观RLC电路的量子特性,取得了一系列的研究成果。本论文的主要工作包括以下内容:
1.利用相干态表象下的Wigner(维格纳)算符和有序算符内的积分(IWOP)技术,重构了奇偶二项式态的Wigner函数。利用Wigner算符与中介态的投影算符之间满足的Radon变换,得到了奇偶二项式态的Tomogram(层析图)函数。借助于数值计算方法,研究了奇偶二项式态所展现的非经典性质,并根据量子态Wigner函数的边缘分布,阐明了此Wigner函数的物理意义。
2.研究了奇偶负二项式态的压缩、反聚束和相位概率分布等非经典性质,并借助Pegg-Barnett相位算符理论和数值计算方法,研究了奇偶负二项式态在数算符和相位算符分量上的压缩特性。利用相干态表象下的Wigner算符和IWOP技术,重构了奇偶负二项式态的Wigner函数,并考察了此Wigner函数的物理意义。利用中介表象理论获得了奇偶负二项式态的Tomogram函数,并详细地讨论了这些量子态所展现出的非经典性质。
3.借助于IWOP技术、相干态表象下的Wigner算符和中介表象理论,重构了Klauder-Perelomov相干态的Wigner函数和Tomogram函数,并详细讨论了它们所展现出的非经典性质。根据Klauder-Perelomov相干态的Wigner函数的边缘分布,阐明了此Wigner函数的物理意义。
4.利用Weyl对应、Wigner理论及相干热态表象理论,探讨了有限温度下介观RLC电路中的电荷与电流的量子涨落,发现其涨落随着温度与电阻的增加而增加,并阐明了Wigner函数边缘分布统计平均的物理意义。
This thesis presents my main research work carried out during my master course.In this thesis,the quantum properties of some quantum states and mesoscopic RLC circuit are investigated.Significant new results as shown below:
1.Using the coherent state representation of Wigner operator and the technique of integration within an ordered product(IWOP) of operators,the Wigner functions of the even and odd binomial states(EOBSs) are obtained.Using the Radon transform between the Wigner operator and the projection operator of intermediate coordinate-momentum state,the tomograms of the EOBSs calculated.By virtue of numerical computation,the nonclassical properties of the EOBSs are studied,then the physical meaning of the Wigner functions for the EOBSs is given by means of their marginal distributions.
2.The properties of the even and odd negative binomial states(NBSs) are investigated. Mainly we concentrate on the nonclassical properties for such the states where we consider the quadrature squeezing,antibunching effect and the phase probability distributions. Using the Pegg-Barnett formalism of phase operator,the phase probability distributions of the states are discussed,and also the phase and number squeezing with different parameters are studied.Using the coherent state representation of Wigner operator and the IWOP technique,the Wigner functions of the even and odd NBSs are obtained.And,the physical meaning of the Wigner functions for the even and odd NBSs is discussed.Then, by virtue of intermediate coordinate-momentum representation,the tomograms of the even and odd NBSs are obtained,and their nonclassical properties exhibited are discussed in detail.
3.Using the IWOP technique、the coherent state representation of Wigner operator and the intermediate coordinate-momentum representation,the Wigner functions and the tomograms of the Klauder-Perelomov(K-P) coherent states for the pseudoharmonic oscillator(PHO) are obtained.The nonclassical properties of the K-P coherent states for the PHO are discussed.Moreover,the physical meaning of the Wigner functions for the K-P coherent states for the PHO is given by means of their marginal distributions.
4.By means of the Weyl correspondence、Wigner theorem and the coherent thermo state representation theorem we show that the quantum fluctuations of both charge and current of mesoscopic RLC circuit at finite temperature,we show that the quantum fluctuations of both charge and current increase with the rising temperature and the resistance value,the physical meaning of its marginal distributions'statistical average is discussed.
1.利用相干态表象下的Wigner(维格纳)算符和有序算符内的积分(IWOP)技术,重构了奇偶二项式态的Wigner函数。利用Wigner算符与中介态的投影算符之间满足的Radon变换,得到了奇偶二项式态的Tomogram(层析图)函数。借助于数值计算方法,研究了奇偶二项式态所展现的非经典性质,并根据量子态Wigner函数的边缘分布,阐明了此Wigner函数的物理意义。
2.研究了奇偶负二项式态的压缩、反聚束和相位概率分布等非经典性质,并借助Pegg-Barnett相位算符理论和数值计算方法,研究了奇偶负二项式态在数算符和相位算符分量上的压缩特性。利用相干态表象下的Wigner算符和IWOP技术,重构了奇偶负二项式态的Wigner函数,并考察了此Wigner函数的物理意义。利用中介表象理论获得了奇偶负二项式态的Tomogram函数,并详细地讨论了这些量子态所展现出的非经典性质。
3.借助于IWOP技术、相干态表象下的Wigner算符和中介表象理论,重构了Klauder-Perelomov相干态的Wigner函数和Tomogram函数,并详细讨论了它们所展现出的非经典性质。根据Klauder-Perelomov相干态的Wigner函数的边缘分布,阐明了此Wigner函数的物理意义。
4.利用Weyl对应、Wigner理论及相干热态表象理论,探讨了有限温度下介观RLC电路中的电荷与电流的量子涨落,发现其涨落随着温度与电阻的增加而增加,并阐明了Wigner函数边缘分布统计平均的物理意义。
This thesis presents my main research work carried out during my master course.In this thesis,the quantum properties of some quantum states and mesoscopic RLC circuit are investigated.Significant new results as shown below:
1.Using the coherent state representation of Wigner operator and the technique of integration within an ordered product(IWOP) of operators,the Wigner functions of the even and odd binomial states(EOBSs) are obtained.Using the Radon transform between the Wigner operator and the projection operator of intermediate coordinate-momentum state,the tomograms of the EOBSs calculated.By virtue of numerical computation,the nonclassical properties of the EOBSs are studied,then the physical meaning of the Wigner functions for the EOBSs is given by means of their marginal distributions.
2.The properties of the even and odd negative binomial states(NBSs) are investigated. Mainly we concentrate on the nonclassical properties for such the states where we consider the quadrature squeezing,antibunching effect and the phase probability distributions. Using the Pegg-Barnett formalism of phase operator,the phase probability distributions of the states are discussed,and also the phase and number squeezing with different parameters are studied.Using the coherent state representation of Wigner operator and the IWOP technique,the Wigner functions of the even and odd NBSs are obtained.And,the physical meaning of the Wigner functions for the even and odd NBSs is discussed.Then, by virtue of intermediate coordinate-momentum representation,the tomograms of the even and odd NBSs are obtained,and their nonclassical properties exhibited are discussed in detail.
3.Using the IWOP technique、the coherent state representation of Wigner operator and the intermediate coordinate-momentum representation,the Wigner functions and the tomograms of the Klauder-Perelomov(K-P) coherent states for the pseudoharmonic oscillator(PHO) are obtained.The nonclassical properties of the K-P coherent states for the PHO are discussed.Moreover,the physical meaning of the Wigner functions for the K-P coherent states for the PHO is given by means of their marginal distributions.
4.By means of the Weyl correspondence、Wigner theorem and the coherent thermo state representation theorem we show that the quantum fluctuations of both charge and current of mesoscopic RLC circuit at finite temperature,we show that the quantum fluctuations of both charge and current increase with the rising temperature and the resistance value,the physical meaning of its marginal distributions'statistical average is discussed.
引文
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[10]Agarwal G.S.,Negative binomial states of the field-operator representation and production by state reduction in optical processes[J].Phys.Rev.A,1992,45(3):1787-1792.
[11]Fan H.Y.,Entangled State Representations in Quantum Mechanics and Their Applications[M](Shanghai:Shanghai Jiao Tong University Press)(in Chinese) 2001.
[12]Fan H.Y.and Li S.,Constructing even-and odd-negative binomial states[J].Commun.Theor.Phys.,2005,43(3):519-522.
[13]Dariano G.M.,Macchiavello C.and Paris M.G.A.,Detection of the density matrix through optical homodyne tomography without filtered back prcjection[J].Phys.Rev.A,1994,50(5):4298-4302.
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[15]Luttervach L.G.and Davidovich L.,Method for direct measurement of the Wigner function in cavity QED and ion traps[J].Phys.Rev.Lett.,1997,78(13):2547-2550.
[16]Zhang Z.M.,Measuring the Wigner functions of two-mode cavity fields and testing the Bell's inequalities[J].Chin.Phys.Lett.,2004,21(1):5-8.
[17]Smithey D.T.,Beck M.and Cooper J.,Measurement of number-phase uncertainty relations of optical fields[J].Phys.Rev.A,1993,48(4):3159-3167.
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[19]Nogues G.,Rauschenbeutel A.and Osnaghi S.et al.,Measurement of a negative value for the Wigner function of radiation[J].Phys.Rev.A,2000,62(5):054101.
[20]Vogel K.and Risken H.,Determination of quasiprobability distribution in terms of probability distributions for the rotated quadrature phase[J],Phys.Rev.A,1989,40(5):2847-2849.
[21]Franca Santos M.,Solano E.and de Matos Filho R.L.,Conditional large Fock state preparation and field state reconstruction in cavity QED[J].Phys.Rev.Lett.,2001,87:093601.
[22]张智明.利用微脉塞重构腔场的Wigner函数[J].物理学报,2004,53(1):70-74..
[23]Zhang Z.M.,A simple scheme for directly measuring the Wigner functions of cavity fields[J].Chin.Phys.Lett.,2003,20(2):227-229.
[24]冯端,金国钧著,凝聚态物理新论,上海科学技术出版社,1992,第五章.
[25]张立德,牟季美著,纳米材料学,沈阳:辽宁科学技术出版社,1994.
[26]Srivastava Y.,Widom A.,Quantum electrodynamic processes in electrical engineering circuit[J].Phys.Rep.,1987,148(1):1-65.
[27]Buot F.A.,Mesoscopic physics and nanoelectronics[J].Phys.Rep.,1993,234(2,3):73-174.
[28]Garcia R.G.,Atomic-scale manipulation in air with the scanning tunneling microscope[J].Appl.Phys.Lett.,1992,60(16):1960-1962.
[29]Caldeira A.O.and Leggett A.J.,Quantum tunneling in a dissipative system[J].Ann.Phys.,1983,149(2):374-456.
[30]Knight P.L.and Allen L.,Concepts of Quantum Optics[M].Pergamon Press,1983,54-69;M.O.Scully,M.S.Zubairy,Quantum Optics[M].Cambridge University Press,1996,46-71.
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