探寻光场热真空态的有序算符内的积分方法

发布时间：2017-12-31 07:14

本文关键词：探寻光场热真空态的有序算符内的积分方法　出处：《中国科学技术大学》2016年博士论文　论文类型：学位论文

【摘要】：自然界中,几乎所有的系统都浸在热库当中。所以系统与热库间产生的能量传递必然会影响系统的激发以及退激发过程。系统中产生的激发量子,有一部分就来源于热库。在系统的温度较高时,属于经典光学范畴,而当温度较低时,则属于量子光学范畴。根据量子力学知识,非零温度下处于热平衡状态的量子态通常用混合态的密度矩阵ρ来描述,物理量A的期望值是通过计算矩阵A和ρ乘积的迹来得到,但是这种方法实际操作起来比较繁复与困难。为了以一种便利的方式研究热库对系统的影响,Takahashi和Umezawa在1975年提出了热场动力学理论,他们引入纯态形式的热真空态概念,于是在温度非零情况下混态的统计平均值可以通过计算纯态的统计平均值得到,其代价是系统的自由度在原有基础上,增加等量的“虚拟”自由度。但是Takahashi和Umezawa仅给出了混沌光场对应的热真空态,并且其方法处在初级阶段。本文将提出构造热真空态的新方法,即在前人已有的部分求迹理论的基础上利用有序算符内的积分技术(简称IWOP技术),可以对不同的复杂物理系统引入相应的热真空态。其优点是：1)计算纯态形式的广义热真空态的期望值可以得到系统力学量的系综平均,简化了量子统计期望值的计算,为研究新光场的性质和在量子通道中的演化规律提供了便利。2)热真空态的引入能体现系统与热库的量子纠缠,便于我们进一步用纠缠态表象来研究系统在各种量子通道中的演化。3)有利于在理论上发现新光场。因此,这一方法丰富和发展了热场动力学理论和量子统计理论。本文的主要内容包括：一、简要介绍了范洪义教授提出的有序算符内的积分技术理论,对算符的正规乘积形式、反正规乘积形式和Weyl排序形式的积分技术进行了讨论,并利用该技术导出了常用量子力学表象完备关系的纯高斯性积分形式和单(双)模压缩算符的正规乘积形式。介绍了范洪义提出的纠缠态表象,Wigner算符和Wigner函数及其在热真空态情况下的计算方法。二、利用IWOP技术从崭新的角度阐述了量子光学中几种常见的光场及其性质,如负二项式态光场、二项-负二项联合分布光场和混沌光场。三、在部分求迹理论的基础上,提出利用IWOP技术和方法导出系统对应的广义热真空态的方法。用热真空态,力学量的系综平均可以转化为计算纯态下的期望值,简化了量子统计计算。并首次利用该方法推导出了负二项式态光场的热真空态。利用负二项式态光场的热真空态很方便计算出光场的平均光子数、光子数涨落、二阶相干度和Wigner函数。四、借助IWOP技术,我们巧妙的将压缩混沌光场的密度算符转化为正规乘积形式,再推导出压缩混沌光场的热真空态,进而给出了压缩混沌光场的平均光子数、光子数涨落、二阶相干度和Wigner函数,在此基础上分析了光场的性质。五、利用混沌光场和负二项式态光场的热真空态,结合IWOP技术研究了纯态下热真空态对算符求平均值的相关规律,分别得到了混沌光场和负二项式态光场对应的平均值定理和平移算符的平均值定理。六、研究了光子扣除压缩混沌光场的热真空态。为了能够求出密度算符的归一化系数,我们先推导出了光场的反正规乘积,然后用P-表示得到其正规乘积,最终在相干态表象下对光场求迹后得到了光场的归一化系数。进而推导出了该光场对应的热真空态、光子数分布和光子数涨落,并分析了光场的性质。七、作为部分求迹方法的另一个应用,我们研究了兼有压缩和混沌效应的双模光场的温度效应。通过分别计算双模光场中每一模的光子数分布,对相应的温度效应提出了合理的物理解释。
[Abstract]:In nature, almost all systems are immersed in the library. So the heat generating system and thermal energy transfer between base will affect the system excitation and de excitation process. The quantum excitation system, a part from the reservoir. In high temperature system, which belongs to the category of classical optics, and when the temperature is low, it belongs to the category of quantum optics. According to quantum mechanics, quantum state density matrix P in thermal equilibrium with non zero temperature is used to describe the mixing state of physical quantity, the expected value of A is calculated by matrix A and P trace of the product to get, but the actual operation method more complicated and difficult. In order to influence in a convenient way of heat reservoir on the system, Takahashi and Umezawa proposed the theory of thermal field dynamics in 1975, they introduced the thermal vacuum state concept of pure state form, so in the temperature Non zero case statistics mixed state average by calculating mean value of the pure state, the cost of the degrees of freedom of the system on the basis of the original, increased amounts of "virtual" degrees of freedom. But Takahashi and Umezawa only gives a chaotic light field corresponding to the thermal vacuum state, and the method in the primary stage. This paper will put forward a new method to construct the thermal vacuum state, based on the previous theory that trace the part on the use of the technique of integration within ordered product (IWOP), can be used in thermal vacuum state corresponding to different complex physical systems. Its advantages are: 1) to calculate the generalized pure thermal vacuum state form the expected value can be obtained by the ensemble average of mechanical quantity system, simplifies the calculation of quantum statistical expectations, provides a convenient.2 for the research field and in Xinguang quantum channel in the evolution of the thermal vacuum state) Quantum entanglement can reflect the system with heat reservoir, we can further use the entangled state representation to study the evolution of.3 system in various quantum channel in) for the discovery of Xinguang field in theory. Therefore, this method enriches and develops the theory of thermal field dynamics and quantum statistical theory. The main contents of this paper include: 1. Briefly introduces the theory of order operator integral technique proposed by Professor Fan Hongyi in the normal product form of the integral operator, reverse normal product form and Weyl sort form are discussed, and use the technology derived pure Gauss integral form commonly used quantum mechanics representation complete relation and single (double) normal product form squeezing operator. The entangled state representation proposed by Fan Hongyi, Wigner operator and Wigner function and its calculation method in thermal vacuum state conditions. Two, using IWOP technology from new angle The light field and expounds several common properties in quantum optics, such as negative binomial state light field, two negative two joint distribution of light field and chaotic light field. The three part, based on trace theory, proposed method of generalized thermal vacuum state by using IWOP technology and method system are derived respectively. In thermal vacuum state, the ensemble average of mechanical quantity can be transformed into the calculation of the pure state expectation, simplifies the calculation of quantum statistics. And for the first time using this method deduced the thermal vacuum state with negative binomial state light field. It is convenient to use in thermal vacuum state with negative binomial state light field average photon field the number of photon number fluctuation, two order coherence and Wigner function. Four, with the help of IWOP technology, the density operator we cleverly squeezed chaotic light field into the normal product form, and then derive the thermal vacuum state light field compression chaos, then gives the chaotic light field compression The average number of photons, the photon number fluctuation, two order coherence degree and Wigner function, based on the analysis of the properties of light field. Five, using chaotic light field and negative binomial state light field in thermal vacuum state, studied the related rules in thermal vacuum state of the pure state operator averaging with IWOP Technology obtained chaotic light field and negative binomial state light field corresponding to the mean value theorem of mean value theorem and shift operator. Six, studied the thermal vacuum state photon subtracted squeezed chaotic light field. In order to calculate the normalized coefficient of density operator, we first derive the light field anti normal product, and then said the normal product with P-, finally in the coherent state representation of the light field trace obtained after normalization coefficient field. Then deduced the light field corresponding to the thermal vacuum state, the photon number distribution and photon number fluctuation, and analyzes the nature of the light field seven, As another application part tracing method, we investigated the effect of temperature on both the two mode light field compression and chaotic effect. By calculating the photon number distribution of each of the first mock exam mode light field respectively, put forward a reasonable physical explanation for temperature effects.

【学位授予单位】：中国科学技术大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O413

【相似文献】