【作者】 吴子瑕；

【导师】 成泽；

【作者基本信息】 华中科技大学 ， 光学， 2009， 博士

【摘要】 在量子光学领域中，光场量子特性的研究一直是人们关注的课题。本文主要研究了克尔非线性黑体中辐射场的统计属性，得出了一些有意义的结论，全文共分为以下五部分：第一部分，研究了克尔非线性黑体光场的振幅平方压缩效应，发现克尔非线性黑体光场在转变温度T_c下可以同时处于振幅压缩和振幅平方压缩态，并且光场的振幅平方压缩效应要比振幅压缩效应大；克尔非线性黑体光场的振幅平方压缩效应随着温度T和克尔非线性系数γ的增加而减小；随着频率ω_?的增大，振幅平方压缩效应先随增大后减小，在频率ω_m=6.7×10¹³s^-1处，振幅平方压缩效应最强；在相同参数下，克尔非线性黑体的某个振幅平方变量比普通黑体的振幅平方变量要小。第二部分，研究了克尔非线性黑体光场的相位对称性。当温度T处于不同范围时，克尔非线性黑体光场处于不同的态。利用准几率分布函数即Q函数分布详细讨论了克尔非线性黑体光场处于不同态的空间相位。发现温度T和克尔非线性系数γ对Q函数分布有很大的影响。随着温度T的降低，克尔非线性黑体热辐射场由常态变为压缩态，光场经历了一个一级相变，其相位对称自发破缺。第三部分，研究了克尔非线性黑体的统计性质。讨论了在温度低于转变温度T_c时克尔非线性黑体光场的二阶关联函数，光子数分布函数以及相位分布函数。研究表明，二阶关联函数g^（2）≥2，即光子表现出经典的群聚效应，光场为超泊松分布，而且温度T，克尔非线性系数γ和频率ω_k对泊松分布统计有很大的影响；光子数分布函数P（n）呈现振动形态，振动行为只发生在光子数少量的情况下，是光场的压缩属性的体现；相位分布函数P（θ）呈现称结构，在±π／2处出现双峰，随着温度T和克尔非线性系数γ的减小，相位分布函数P（θ）的振幅增大，波宽变窄，即光场的压缩效应越来越强。同时，给出了这些量的测量方法。第四部分，研究了克尔非线性黑体辐射场的非经典程度。分别采用两种方法，即Lee的相位式法和Malbouisson的距离式衡量法讨论了在温度低于转变温度T_c时，辐射场的非经典程度。相比较而言，Lee的相位式衡量法比较复杂，不易于处理。同时发现随着温度T和克尔非线性系数γ以及频率ω_k的增大，克尔非线性黑体辐射场的非经度降低；并且克尔非线性黑体辐射场的非经典度比普通黑体的非经典度要高。第五部分，研究了带电谐振子与克尔非线性黑体相互作用的耦合系统。带电谐振子处于谐势井中，在偶极耦合下与光场发生相互作用。通过海森堡运动方程，建立了谐振子的朗之万方程。研究表明，当温度低于转变温度T_c时，量子朗之万方程的记忆函数是温度T和克尔非线性系数γ的递减函数；在大的截止频率极限下，在克尔非线性黑体中所观测到的谐振子质量和自由能位移要比普通黑体中的谐振子质量和自由能位移大。自由能位移不再简单的与T²成正比。在普通黑体中，谐振子的能级位移是负值，但是在克尔非线性黑体中，只是在零温度附近，能级位移是负值，而在接近转变温度的情况下，能级位移是一个很大的正值。当温度高于转变温度T_c时，其结论跟普通黑体中的情况一样。更多还原

【Abstract】 The characteristics of quantum field have attracted much attention in the area ofquantum optics. The statistical properties of radiation thermal field in a Kerr nonlinearblackbody have been investigated, and some significative and new results have obtained.There are five parts in this thesis.First, the photon field in a Kerr-nonlinear blackbody is in an amplitude-squaredsqueezed state. The amplitude-squared squeezing effect enhances with increasingtemperature T and parameterγ. As frequencyω_k increases, the amplitude-squaredsqueezing effect firstly enhances as frequencyω_k increases. Atω_m=6.7×10¹³s^-1, theamplitude-squared squeezing effect is strongest, then the squeezing effect weakens as asfrequencyω_k increases. The amount of the amplitude-squared squeezing in aKerr-nonlinear blackbody is much larger than the corresponding squeezing in normalblackbody, and the degree of amplitude-squared squeezing is much larger than theamplitude squeezing for the same range of parameters in a Kerr-nonlinear blackbody.Second, the phase symmetry breaking is investigated in a Kerr-nonlinear blackbodyin terms of the quasiprobability distribution. The quasiprobability （Q function）distribution is discussed in detail in the different ranges of temperature T. It is foundthat the distribution of Q function strongly depends on the temperature T and couplingparameterγ. Non-classical effects of quadrature squeezing have been observed. In thetransition from the normal to the squeezed thermal radiation state, the phase symmetry ofthe photon system in a Kerr-nonlinear blackbody is spontaneously broken.Third, we study the statistical properties of thermal radiation in a Kerr nonlinearblackbody. The second-order correlation function, the phase space distribution function and the photon number distribution are considered. It is found that blow a transitiontemperature T-c, the second-order correlation function g² （0）≥2, which shows that thephoton system is classical bunching, and the statistical behavior always super-Poissonianin the Kerr-nonlinear blackbody, and the super-Poissonian statistics are stronglydependent on the temperature T and the coupling parameterγ; the photon numberdistribution P（n） presents nonclassical oscillations, while the oscillatory behaviorsonly occur at very low number of photons, which shows the photon filed in a Kerrnonlinear blackbody is in a squeezed state; the phase distribution P（θ） has a doubletstructure and the peaks are at±π/2, but with broader width and more significantamplitude as the temperature T and the coupling parameterγincrease.Fourth, the degree of nonclassicality of a photon field is considered in a Kerrnonlinear blackbody. The space-phase and distance-type measures are employed,respectively. It is shown that blow a transition temperature T_c, the photon field becomesless nonclassical in the Kerr-nonlinear blackbody as temperature T, Kerr nonlinearcoefficientγand frequencyω_k increase. Furthermore, the degree of nonclassicality of aKerr nonlinear blackbody is always higher than that of a normal blackbody.Fifth, we derive a quantum Langevin equation for the macroscopic description of acharged oscillator in a harmonic potential well interacting with a Kerr nonlinearblackbody radiation field via dipole coupling. It is shown that below a transitiontemperature T_c, the memory function in our quantum Langevin equation is a decreasingfunction of temperature T and Kerr nonlinear coefficientγ. In the large-cutoff limit, theobserved mass and free energy shift of a charged oscillator in a Kerr nonlinear blackbodyare larger than those in a normal blackbody. The free energy shift is a complex functionof temperature which is no longer a simply T²-dependent function. The energy level shift of an oscillator in a normal blackbody is a negative, while in our Kerr nonlinearblackbody, only near zero temperature the corresponding energy level shift is a negative.As the temperature increases to transition temperature T, the corresponding energy levelshift becomes a large positive value. Above T_c, our results are the same as those in anormal blackbody.更多还原