本文關(guān)鍵詞：探尋光場(chǎng)熱真空態(tài)的有序算符內(nèi)的積分方法　出處：《中國(guó)科學(xué)技術(shù)大學(xué)》2016年博士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 熱真空態(tài) 負(fù)二項(xiàng)式態(tài)光場(chǎng) 壓縮混沌光場(chǎng) 平均值定理 光子扣除壓縮混沌光場(chǎng) 溫度效應(yīng) 衰減通道

【摘要】：自然界中,幾乎所有的系統(tǒng)都浸在熱庫(kù)當(dāng)中。所以系統(tǒng)與熱庫(kù)間產(chǎn)生的能量傳遞必然會(huì)影響系統(tǒng)的激發(fā)以及退激發(fā)過(guò)程。系統(tǒng)中產(chǎn)生的激發(fā)量子,有一部分就來(lái)源于熱庫(kù)。在系統(tǒng)的溫度較高時(shí),屬于經(jīng)典光學(xué)范疇,而當(dāng)溫度較低時(shí),則屬于量子光學(xué)范疇。根據(jù)量子力學(xué)知識(shí),非零溫度下處于熱平衡狀態(tài)的量子態(tài)通常用混合態(tài)的密度矩陣ρ來(lái)描述,物理量A的期望值是通過(guò)計(jì)算矩陣A和ρ乘積的跡來(lái)得到,但是這種方法實(shí)際操作起來(lái)比較繁復(fù)與困難。為了以一種便利的方式研究熱庫(kù)對(duì)系統(tǒng)的影響,Takahashi和Umezawa在1975年提出了熱場(chǎng)動(dòng)力學(xué)理論,他們引入純態(tài)形式的熱真空態(tài)概念,于是在溫度非零情況下混態(tài)的統(tǒng)計(jì)平均值可以通過(guò)計(jì)算純態(tài)的統(tǒng)計(jì)平均值得到,其代價(jià)是系統(tǒng)的自由度在原有基礎(chǔ)上,增加等量的“虛擬”自由度。但是Takahashi和Umezawa僅給出了混沌光場(chǎng)對(duì)應(yīng)的熱真空態(tài),并且其方法處在初級(jí)階段。本文將提出構(gòu)造熱真空態(tài)的新方法,即在前人已有的部分求跡理論的基礎(chǔ)上利用有序算符內(nèi)的積分技術(shù)(簡(jiǎn)稱IWOP技術(shù)),可以對(duì)不同的復(fù)雜物理系統(tǒng)引入相應(yīng)的熱真空態(tài)。其優(yōu)點(diǎn)是：1)計(jì)算純態(tài)形式的廣義熱真空態(tài)的期望值可以得到系統(tǒng)力學(xué)量的系綜平均,簡(jiǎn)化了量子統(tǒng)計(jì)期望值的計(jì)算,為研究新光場(chǎng)的性質(zhì)和在量子通道中的演化規(guī)律提供了便利。2)熱真空態(tài)的引入能體現(xiàn)系統(tǒng)與熱庫(kù)的量子糾纏,便于我們進(jìn)一步用糾纏態(tài)表象來(lái)研究系統(tǒng)在各種量子通道中的演化。3)有利于在理論上發(fā)現(xiàn)新光場(chǎng)。因此,這一方法豐富和發(fā)展了熱場(chǎng)動(dòng)力學(xué)理論和量子統(tǒng)計(jì)理論。本文的主要內(nèi)容包括：一、簡(jiǎn)要介紹了范洪義教授提出的有序算符內(nèi)的積分技術(shù)理論,對(duì)算符的正規(guī)乘積形式、反正規(guī)乘積形式和Weyl排序形式的積分技術(shù)進(jìn)行了討論,并利用該技術(shù)導(dǎo)出了常用量子力學(xué)表象完備關(guān)系的純高斯性積分形式和單(雙)模壓縮算符的正規(guī)乘積形式。介紹了范洪義提出的糾纏態(tài)表象,Wigner算符和Wigner函數(shù)及其在熱真空態(tài)情況下的計(jì)算方法。二、利用IWOP技術(shù)從嶄新的角度闡述了量子光學(xué)中幾種常見(jiàn)的光場(chǎng)及其性質(zhì),如負(fù)二項(xiàng)式態(tài)光場(chǎng)、二項(xiàng)-負(fù)二項(xiàng)聯(lián)合分布光場(chǎng)和混沌光場(chǎng)。三、在部分求跡理論的基礎(chǔ)上,提出利用IWOP技術(shù)和方法導(dǎo)出系統(tǒng)對(duì)應(yīng)的廣義熱真空態(tài)的方法。用熱真空態(tài),力學(xué)量的系綜平均可以轉(zhuǎn)化為計(jì)算純態(tài)下的期望值,簡(jiǎn)化了量子統(tǒng)計(jì)計(jì)算。并首次利用該方法推導(dǎo)出了負(fù)二項(xiàng)式態(tài)光場(chǎng)的熱真空態(tài)。利用負(fù)二項(xiàng)式態(tài)光場(chǎng)的熱真空態(tài)很方便計(jì)算出光場(chǎng)的平均光子數(shù)、光子數(shù)漲落、二階相干度和Wigner函數(shù)。四、借助IWOP技術(shù),我們巧妙的將壓縮混沌光場(chǎng)的密度算符轉(zhuǎn)化為正規(guī)乘積形式,再推導(dǎo)出壓縮混沌光場(chǎng)的熱真空態(tài),進(jìn)而給出了壓縮混沌光場(chǎng)的平均光子數(shù)、光子數(shù)漲落、二階相干度和Wigner函數(shù),在此基礎(chǔ)上分析了光場(chǎng)的性質(zhì)。五、利用混沌光場(chǎng)和負(fù)二項(xiàng)式態(tài)光場(chǎng)的熱真空態(tài),結(jié)合IWOP技術(shù)研究了純態(tài)下熱真空態(tài)對(duì)算符求平均值的相關(guān)規(guī)律,分別得到了混沌光場(chǎng)和負(fù)二項(xiàng)式態(tài)光場(chǎng)對(duì)應(yīng)的平均值定理和平移算符的平均值定理。六、研究了光子扣除壓縮混沌光場(chǎng)的熱真空態(tài)。為了能夠求出密度算符的歸一化系數(shù),我們先推導(dǎo)出了光場(chǎng)的反正規(guī)乘積,然后用P-表示得到其正規(guī)乘積,最終在相干態(tài)表象下對(duì)光場(chǎng)求跡后得到了光場(chǎng)的歸一化系數(shù)。進(jìn)而推導(dǎo)出了該光場(chǎng)對(duì)應(yīng)的熱真空態(tài)、光子數(shù)分布和光子數(shù)漲落,并分析了光場(chǎng)的性質(zhì)。七、作為部分求跡方法的另一個(gè)應(yīng)用,我們研究了兼有壓縮和混沌效應(yīng)的雙模光場(chǎng)的溫度效應(yīng)。通過(guò)分別計(jì)算雙模光場(chǎng)中每一模的光子數(shù)分布,對(duì)相應(yīng)的溫度效應(yīng)提出了合理的物理解釋。
[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.

【學(xué)位授予單位】：中國(guó)科學(xué)技術(shù)大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：O413

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