Theoretical Study On Quantum Correlation And Geometrical Phases Of Quantum Dots System Via Quantum Point Contact Detect

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.