【作者】 刘宝盈；

【导师】 石康杰； 杨志勇；

【作者基本信息】 西北大学 ， 光学， 2006， 博士

【摘要】 本文构造了经典强度、经典振幅和经典相位具有任意空间分布的非对称四态、五态和九态等多态叠加多模泛函相干态的叠加态光场,利用新近建立的多模压缩态理论,系统研究了上述三种不同的多态叠加多模泛函叠加态光场的广义非线性等幂次与不等幂次高次压缩特性,由此获得了一系列不同于现有报道的新的结果和结论。本文的主要工作内容和研究结果如下: 1.给出了多模泛函相干态及其相反态、多模复共轭泛函相干态及其相反态、多模泛函虚相干态及其相反态、多模泛函虚共轭相干态及其相反态这八个不同的多模光场的光子湮灭算符本征态的解析表达式;从理论上证明:上述八个不同的多模泛函相干态具有非正交性和超完备性,其光子统计分布都符合泊松分布,并能够反映实际激光场经典强度、经典振幅和经典相位的空间分布特征。 2.根据量子力学中的态叠加原理,构造了由多模泛函相干态和多模复共轭泛函相干态及其相反态所组成的非对称四态叠加多模泛函叠加态光场|ψ^（4）（f_j）>_q。给出了利用双孔光网络广义M-Z干涉仪装置制备态|ψ^（4）（f_j）>_q以及利用双孔光网络广义M-Z干涉仪制备多模压缩态光场的理论方案。利用多模压缩态理论,研究了态|ψ^（4）（f_j）>_q的广义非线性等幂次高次振幅压缩特性、等幂次高次和压缩特性、不等幂次高次振幅压缩特性以及不等幂次高次和压缩特性。结果发现:（1）态|ψ^（4）（f_j）>_q是一种典型的多模非经典光场,它在一定条件下可分别呈现出广义非线性等幂次与不等幂次高次振幅压缩效应、高次和压缩效应等等;（2）导致态|ψ^（4）（f_j）>_q呈现上述高次压缩现象的根本原因,就在于态|ψ^（4）（f_j）>_q中各组分之间的态间量子干涉现象、模间量子干涉现象、模间的多光子量子纠缠现象、态|ψ^（4）（f_j）>_q中不同宏观量子态之间的量子纠缠现象以及模间和态间的混合量子纠缠现象。这些量子干涉效应和量子纠缠行为使叠加态中各不同量子态之间以及各不同纵模之间产生竞争效应,其结果导致了各模的经典初绐相位、态间的初始相位差等分别呈现出了各自的经典与非经典量子关联特性,最终导致了光场压缩现象的产生;（3）光场经典强度、经典振幅和经典初始相位的任意空间分布特征对态|ψ^（4）（f_j）>_q的广义非线性等幂次与不等幂次高次压缩现象的压缩程度、压缩深度和压缩幅度等具有直接影响。从而表明:多模压缩态等非经典光场具有一定的空间结构和空间分布,并且这种分布在空间是非均匀、非线性和各向异性的。更多还原

【Abstract】 In this thesis, the asymmetrical multi-state superposition multimode functional superposition state light-field, such as the asymmetrical four-, five- and nine-state superposition multimode functional superposition state light-field for which the classical intensity, the classical amplitude and the classical phase of the components in the states mentioned above have any spatial distribution, are constructed according to the state superposition principle in quantum mechanics. By utilizing the multimode squeezed state theory established recently, the generalized nonlinear equal- and unequal-power higher-power squeezing properties of the three kinds of multi-state superposition multimode functional superposition state light-fields are studied systematically. A series of new results and conclusions are therefore obtained, which are rather different from the latest reports. The main research contents and results are as the following:1. The analytical expressions of the eight different eigenstates of photon annihilation operator are given in this thesis. They are called the multimode functional coherent state and its contrary state, the multimode complex conjugate functional coherent state and its contrary state, the multimode functional imaginary coherent state and its contrary state, and the multimode imaginary conjugate functional coherent state and its contrary state, respectively. It is proved that these eight different multimode functional coherent states have the properties of non-orthogonally and over-completeness: And also they can present the property of Sub-poissionian photon statistics. So the eight states can be used to characterize any spatial distribution characteristic of classical intensity, classical amplitude, and classical initial phase of practical laser fields.2. The four-state superposition multimode functional superposition stateisconstructed, that is composed of the multimode functional coherent state, the multimode complex conjugate functional coherent state, and their contrary states. The theoretical scheme for preparing the state and for preparing multimode squeezed statelight-fields are given based upon the model of two-port light network generalized M-Z (Mach-Zehnder) interferometer. Using the multimode squeezed state theory, the properties of generalized nonlinear equal-power higher-power amplitude squeezing, equal-power higher-power sum squeezing, unequal-power higher-power amplitude squeezing, and unequal-power higher-power sum squeezing of the state are studied in detail,respectively. It is found that, (1) The state is a typical multimode non-classicallight-field, it can respectively present generalized nonlinear equal- and unequal-power higher-power amplitude squeezing and sum squeezing effect under some certain and fixed conditions. (2)The essential reason causing in the state ^(4)(/.)\ to display generalizedJ Iqqnonlinear higher-power squeezing phenomena lies in the quantum interference effects and quantum entanglement effects among the components in the state i//w(f,)) , the quantumJ Iqinterference effects and quantum entanglement effects among different modes in the state \\f/w(f )\ , multi-photon quantum entanglement effects among different photons of eachI / I qmode in the state ipw(fj)) , and mixed quantum entanglement effects among different state and different mode in the stateintensity and classical amplitude of light-field have Gaussian distribution features (diffraction beams) and other non-diffraction beams (such as cosine light beams).4. The state t//(A)(f)) is constructed, and its generalized nonlinear equal-powerhigher-power difference squeezing effect is studied by using multimode squeezed state theory. It is found that the two quadrature components of this state can present symmetrical lth-power difference squeezing effect under some certain and fixed conditions while each macroscopical quantum state within the state u/(4)(/.)) is two-mode light-field. However,the state y/w(f)\ never present difference squeezing effect if the cavity-mode-numberJ 11qis larger than two, or squeezed power-number is larger than one. This is a special physical phenomenon that needs further research.5. The unequal-intensity and injected vacuum field asymmetrical five-state superposition multimode functional superposition state light-field i//(5\f)) is constructed,and the theoretical scheme for preparing the state ?^i)(/)\ for which the two-port lightnetwork generalized M-Z interferometer is used are given. The generalized nonlinear equal-power higher-power amplitude squeezing properties of the state mentioned is studied in detail by utilizing multimode squeezed state theory. It is found that, for the state y/w(fj))q, injected multimode vacuum states light-field can enhance the squeezedamplitude, the squeezed degree and the squeezed depth, and thereby enhance the squeezing effect of the multimode light-fields under fixed conditions.6. The unequal-intensity and injected vacuum field asymmetrical nine-state superposition multimode functional superposition state light-field i//{^(f)) is constructed.was j I yThe generalized nonlinear equal-power higher-power amplitude squeezing properties of the state is studied preliminary, and the results are universal for studying the squeezed properties of various multimode superposition state light fields.From the above, we can see that the results in this thesis may be important for the further research of generating, preparing, controlling and dominating multimode squeezed states light-field, quantum communication, and multimode light-quanta communication.更多还原