量子点系统量子关联和几何相点接触探测的理论研究
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摘要
二十世纪之初,在试图对微观世界的物理现象进行描述时,人们发现已经完善的经典力学理论在解释微观实验现象时变得十分荒谬。人们逐渐意识到微观世界的运行规律和经典的宏观世界是截然不同的,在不断的尝试中量子力学诞生了。在百年的发展中量子力学展示出了巨大的力量,并在物理学的不同领域硕果累累。二十世纪末,在经典信息论和量子理论的结合中产生了一个新兴学科—量子信息论。
在对量子体系的探测过程中由于探测器件和量子系统的作用使得量子系统成为一个开放系统,在获得体系量子信息的同时系统的能量和相干性也将受到耗散。本论文以量子点系统的点接触探测作为研究对象,研究探测电流输出和系统的纠缠及量子关联的关系,以及探测对体系的几何相位的影响并提出一种几何相位的探测方案。
第一章和第二章是本论文的第一部分。在这一部分中,我们首先对量子力学和量子信息学中的物理概念和历史进行介绍,之后我们对论文中用到的物理概念和方法进行简要的说明。在介绍量子点概念及其描述方法后,我们对本论文中所用到的处理量子点接触系统的Bloch速率方程方法和粗粒噪声进行说明。在这一部分的最后我们介绍研究点接触探测过程中用到的negativity,量子discord和混态几何相位概念和计算方法。
第三章是本论文的第二部分。在这部分中我们提出一个通过点接触探测过程读取量子点系统中的纠缠和量子discord信息的方案。在介绍了模型的主方程和探测器的输出电流后,我们利用数值方法研究体系和电流以及纠缠和量子discord演化动力学。通过对体系动力学的模拟,我们发现探测器的输出电流和体系的纠缠及量子discord具有相似的演化性质。因此利用这个模型,可以通过探测电流的极大值点来确定系统具有最大纠缠和量子discord的时刻。同时,分析了探测器对体系的纠缠和量子discord的耗散作用。最后我们利用输出电流的粗粒噪声分析探测方案的实际可行性。
第四章是本论文的第三部分。在这一章中我们分析受单电子晶体管结构的点接触探测器作用下的一个内部存在库仑相互作用的双量子点比特系统的几何相位性质。在这个模型中点接触探测器是作为环境引入的。在给出系统的速率方程描述之后,我们分析了探测过程和体系内的库仑相互作用对子系统几何相位的影响。我们发现探测器对量子比特系统几何相位的影响是通过其中心量子点的电子占据情况来作用的。而库仑相互作用对子系统几何相位的影响表现在两个方面。一方面库仑相互作用使两个比特都获得能量的增加,从而各自演化获得的几何相位增加。另一方面库仑相互作用造成的两个电子之间的弱”碰撞”,使得两个子系统的几何相位受到一定的破坏。
在第五章中,我们通过点接触探测电流和系统内部状态之间的关系,在弱退相干近似下得到了一个通过电流函数积分形式表示系统几何相位的方案。不同于几何相位的干涉测量方式,点接触探测不会破坏系统的几何相位。电流积分表示中的参数是能够通过实验确定的。我们通过对探测电流的粗粒噪声以及信噪比的分析说明探测方案的实际可行性。结果表明,在弱探测下探测电流函数积分在较短时间内能够比较准确的反映出系统的几何相位,同时探测电流的信噪比也是较大的。
最后,我们给出了本文的总结和展望。
At the beginning of the20th century, people who tried to explain the microscopic physical phenomena, found that the results they got were absurd when they attempted to interpret the output of microscopic experiments with consummate classic theory of physics.People found that the rules of microscopic world are quite different from the classical counterparts gradually. In order to understand the microscopic world, the quantum mechanics was born. With more than100years of development, quantum theory shows great power, and fruitful in many different scientific areas. At the end of20th century, combining quantum theory with classic information theory the quantum information emerges.
In the process of detecting the quantum system, because of the interaction between quantum system and the detector, the system is open. While we try to extract the quantum information of the system, the quantum system will suffer from dissipations of energy and coherence simultaneously. In this thesis we choose the process of point detection of quantum dots system as our topic. We find out the connection between the current through the quantum point contact detectors and the entanglement, quantum discord dynamics of the system. Furthermore, we study the influence of the detection on the geometrical phases of the system, and the method to measuring geometrical phase with a quantum point contact device.
In chap.1and chap.2, we introduce the histories and concepts of quantum mechanics, quantum information, measurement, quantum open system and quantum noise. Then we introduce the methods and other physical concepts that will be used in this dissertation. After the introduction of the concept of quantum dot and the method to depict it, we introduce the rate equation method of the point detect systems and Shot noise. At the end of this part we introduce the conceptions of negativity, quantum discord, geometrical phase of a mixed state system and the method to calculating them.
In chap.3we propose a scheme to read out the entanglement and quantum discord infor-mation by measuring the current through the detector. After introducing the rate equation of the model and the current though the detector, we numerically calculate the dynamics of entanglement, quantum discord and the current of the system. We find that the behaviors of the current and the entanglement,quantum discord of the system are similar. In this model, the time points of when the system gets to its maximal entanglement states can be deter-mined by the summits of the current. In addition, the dissipative effect of detection on the entanglement and quantum discord of the system has been analyzed. Finally, we study the feasibility of the detecting scheme via the shot noise of the current through the detector.
In chap.4. We analyze the geometrical phases of a system which is composed of two double quantum dot bits and a single electronic transistor as a detector. There is Coulomb interaction between the two electrons in each qubit. In this model the quantum point detector is viewed as an environment. After introducing the rate equation of the system we analyze the geometrical phases which are influenced by the detection and the Coulomb interaction between the two qubits. We find that the detector influence the geometrical phase via oc-cupation of the quantum by an electron in it. And the influence of Coulomb interaction has two effects. One is the Coulomb interaction makes both qubits have more energy and enlarge the geometrical phase through the development. The other one is the weak "collision" of the two electrons in each qubit demolishs the geometrical phases weakly.
In chap.5, by using the relation between the current through quantum point detector and the state of the system, we proposed a scheme to express the geometrical phase of the system by a time integral form of the function of the current under the approximation of weak decoherence. Different from the interferometry measurement scheme of the geometrical phase, the point detect method does not damage the geometrical phase of the system. The parameters of the integral form can be determined by experiment. We studied the feasibility of the scheme by analyzing the shot noise and the Signal-to-noise ratio of the current. As a result the integral form of the function of current can depict the geometrical phase of the system under weak measurement within a short time interval. Meanwhile the signal-to-noise ratio of the current is good.
Finally, the conclusions and discussion are given.
在对量子体系的探测过程中由于探测器件和量子系统的作用使得量子系统成为一个开放系统,在获得体系量子信息的同时系统的能量和相干性也将受到耗散。本论文以量子点系统的点接触探测作为研究对象,研究探测电流输出和系统的纠缠及量子关联的关系,以及探测对体系的几何相位的影响并提出一种几何相位的探测方案。
第一章和第二章是本论文的第一部分。在这一部分中,我们首先对量子力学和量子信息学中的物理概念和历史进行介绍,之后我们对论文中用到的物理概念和方法进行简要的说明。在介绍量子点概念及其描述方法后,我们对本论文中所用到的处理量子点接触系统的Bloch速率方程方法和粗粒噪声进行说明。在这一部分的最后我们介绍研究点接触探测过程中用到的negativity,量子discord和混态几何相位概念和计算方法。
第三章是本论文的第二部分。在这部分中我们提出一个通过点接触探测过程读取量子点系统中的纠缠和量子discord信息的方案。在介绍了模型的主方程和探测器的输出电流后,我们利用数值方法研究体系和电流以及纠缠和量子discord演化动力学。通过对体系动力学的模拟,我们发现探测器的输出电流和体系的纠缠及量子discord具有相似的演化性质。因此利用这个模型,可以通过探测电流的极大值点来确定系统具有最大纠缠和量子discord的时刻。同时,分析了探测器对体系的纠缠和量子discord的耗散作用。最后我们利用输出电流的粗粒噪声分析探测方案的实际可行性。
第四章是本论文的第三部分。在这一章中我们分析受单电子晶体管结构的点接触探测器作用下的一个内部存在库仑相互作用的双量子点比特系统的几何相位性质。在这个模型中点接触探测器是作为环境引入的。在给出系统的速率方程描述之后,我们分析了探测过程和体系内的库仑相互作用对子系统几何相位的影响。我们发现探测器对量子比特系统几何相位的影响是通过其中心量子点的电子占据情况来作用的。而库仑相互作用对子系统几何相位的影响表现在两个方面。一方面库仑相互作用使两个比特都获得能量的增加,从而各自演化获得的几何相位增加。另一方面库仑相互作用造成的两个电子之间的弱”碰撞”,使得两个子系统的几何相位受到一定的破坏。
在第五章中,我们通过点接触探测电流和系统内部状态之间的关系,在弱退相干近似下得到了一个通过电流函数积分形式表示系统几何相位的方案。不同于几何相位的干涉测量方式,点接触探测不会破坏系统的几何相位。电流积分表示中的参数是能够通过实验确定的。我们通过对探测电流的粗粒噪声以及信噪比的分析说明探测方案的实际可行性。结果表明,在弱探测下探测电流函数积分在较短时间内能够比较准确的反映出系统的几何相位,同时探测电流的信噪比也是较大的。
最后,我们给出了本文的总结和展望。
At the beginning of the20th century, people who tried to explain the microscopic physical phenomena, found that the results they got were absurd when they attempted to interpret the output of microscopic experiments with consummate classic theory of physics.People found that the rules of microscopic world are quite different from the classical counterparts gradually. In order to understand the microscopic world, the quantum mechanics was born. With more than100years of development, quantum theory shows great power, and fruitful in many different scientific areas. At the end of20th century, combining quantum theory with classic information theory the quantum information emerges.
In the process of detecting the quantum system, because of the interaction between quantum system and the detector, the system is open. While we try to extract the quantum information of the system, the quantum system will suffer from dissipations of energy and coherence simultaneously. In this thesis we choose the process of point detection of quantum dots system as our topic. We find out the connection between the current through the quantum point contact detectors and the entanglement, quantum discord dynamics of the system. Furthermore, we study the influence of the detection on the geometrical phases of the system, and the method to measuring geometrical phase with a quantum point contact device.
In chap.1and chap.2, we introduce the histories and concepts of quantum mechanics, quantum information, measurement, quantum open system and quantum noise. Then we introduce the methods and other physical concepts that will be used in this dissertation. After the introduction of the concept of quantum dot and the method to depict it, we introduce the rate equation method of the point detect systems and Shot noise. At the end of this part we introduce the conceptions of negativity, quantum discord, geometrical phase of a mixed state system and the method to calculating them.
In chap.3we propose a scheme to read out the entanglement and quantum discord infor-mation by measuring the current through the detector. After introducing the rate equation of the model and the current though the detector, we numerically calculate the dynamics of entanglement, quantum discord and the current of the system. We find that the behaviors of the current and the entanglement,quantum discord of the system are similar. In this model, the time points of when the system gets to its maximal entanglement states can be deter-mined by the summits of the current. In addition, the dissipative effect of detection on the entanglement and quantum discord of the system has been analyzed. Finally, we study the feasibility of the detecting scheme via the shot noise of the current through the detector.
In chap.4. We analyze the geometrical phases of a system which is composed of two double quantum dot bits and a single electronic transistor as a detector. There is Coulomb interaction between the two electrons in each qubit. In this model the quantum point detector is viewed as an environment. After introducing the rate equation of the system we analyze the geometrical phases which are influenced by the detection and the Coulomb interaction between the two qubits. We find that the detector influence the geometrical phase via oc-cupation of the quantum by an electron in it. And the influence of Coulomb interaction has two effects. One is the Coulomb interaction makes both qubits have more energy and enlarge the geometrical phase through the development. The other one is the weak "collision" of the two electrons in each qubit demolishs the geometrical phases weakly.
In chap.5, by using the relation between the current through quantum point detector and the state of the system, we proposed a scheme to express the geometrical phase of the system by a time integral form of the function of the current under the approximation of weak decoherence. Different from the interferometry measurement scheme of the geometrical phase, the point detect method does not damage the geometrical phase of the system. The parameters of the integral form can be determined by experiment. We studied the feasibility of the scheme by analyzing the shot noise and the Signal-to-noise ratio of the current. As a result the integral form of the function of current can depict the geometrical phase of the system under weak measurement within a short time interval. Meanwhile the signal-to-noise ratio of the current is good.
Finally, the conclusions and discussion are given.
引文
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