Research On Characteristics Of The Geometric Phase In The Double Quantum Dot System

Since the idea has been proposed that using quantum mechanics could realize quantum computing and quantum information processing,the academic community has set off a research boom in information science and computer science.At the same time,with the continuous shrinking of scale of the devices in the experiments,the effects and the laws of quantum mechanics are constantly being explored and demonstrated.In the realistic implementations of quantum computation and quantum information,the quantum system interacts inevitably with the surrounding environments or the detector,and then the coherence of the system is highly susceptible to be destroyed,resulting in the phenomenon that the information makes mistakes in the process of its input,transmission and reading.For this situation,many researchers spend a lot of energy and time trying to find effective ways to resist decoherence of the system and achieve quantum error correction.In the process,it is found that the geometric phase depends only on the geometry of the path traced by the system,which can be used to design the fault-tolerant quantum logic gate and then ignore some certain types of errors in the evolution of the system,so as to ensure the smooth and accurate transmission information.Besides,in the development of the quantum computer,the double quantum dot(DQD)system is a promising candidate for realizing a qubit on account of its long coherent time and powerful controllability.Therefore,it is of great value to study the geometric phase of this system for designing quantum logic gates,researching the quantum computer and developing the quantum information theory when it interacts with the external environments and a measuring device.The main purpose of this letter is to study the properties of the geometric phase of the double quantum dot(DQD)system in the pure dephasing and dissipative environments by using the quantum point contact(QPC)as a detector.We calculate the geometric phase of an open DQD system according to the kinematic approach of the geometric phase given in the mixed states under nonunitary evolution and the Bloch-type rate equations in order to investigate the influences of the QPC and these two environments on it.We analyse the relationship between the geometric phase of an open DQD system and its evolution path by combining the change of the evolution path of the quantum state in the Bloch sphere representation.The results show that the more obvious the change of the evolution path is,the more obvious the change of the geometric phase is.Then according to the relationship between the geometric phase and the coupling strength between the two quantum dots in the quasiperiod,we find that in these two environments,the coupling strength between the two quantum dots has an enhanced effect on the geometric phase.This is because the increase of the coupling strength between the two quantum dots could widen the width of the tunneling channel connecting these two quantum dots and accelerate the oscillations of the electron between the left and right quantum dots.The frequency and the amplitude of the oscillation of the probabilities of finding the electron in the left or right quantum dot during the quasiperiod would increase,which indicates that the evolution path represented by it becomes longer and its radius becomes bigger in the Bloch sphere representation,leading to the increase of the geometric phase.We also find that the curves of the geometric phase with the coupling strength have a crossover for different decoherence rates,which is related to the mutual restriction of the QPC and the coupling strength on the oscillations of the electron between the two quantum dots.In addition,because the stronger coupling between the system and the QPC causes the electron to be frozen in the one quantum dot,the localization of electrons is enhanced and the solid angle enclosed by the evolution path is almost zero.Finally,the geometric phase with the coupling strength presents a notable near-zero region,which is associated with the quantum Zeno effect.Furthermore,we also discuss the effects of these two environments on the geometric phase.As the results show,in the pure dephasing environment,the geometric phase is suppressed as the dephasing rate increases which is caused by the phase loss of the system.For the dissipative environment,the geometric phase is reduced with the increase of the relaxation rate which is due to the energy dissipation and the phase damping of the system.There are five chapters in this paper which study mainly the geometric phase of the DQD coupled to a QPC in the pure dephasing and dissipative environments.We focus on the evolution of the geometric phase and the physical effects of the QPC and the environments on it.In the first chapter,we introduce mainly the background and the present situation of the geometric phase,including the achievements of the geometric phase of the DQD system.We also elaborate the relationship between the geometric phase and the quantum computer,and the structures and characteristics of the DQD and the QPC.The second chapter is about the theoretical background of the geometric phase.We introduce the proposal and promotion of the Berry phase in detail,including the geometric phase in the evolution of the non-adiabatic cyclic and the non-cyclic.Moreover,some examples related to the physical phenomena of the geometric phase are listed,such as the Aharonov-Bohm effect and the Mobius Band.Further,we introduce the geometric phase in a mixed state,especially the geometric phase under nonunitary evolution.This is important for the subsequent calculation of the geometric phase in an open DQD system.In the third chapter,we describe the theoretical model of the DQD system coupled to a QPC,including its Bloch-type rate equations and the evolution process.Based on the kinematic approach of the geometric phase in the mixed states under nonunitary evolution and the Bloch-type rate equations,the geometric phase of the DQD system in pure dephasing environment is calculated and its images with the coupling strength between the two quantum dots are simulated.We discuss the evolution of the geometric phase for the different decoherence rates and the different dephasing rates.Combining the geometric properties of the path traced by the system,the effects of the QPC and the pure dephasing environment on it are analyzed.In the fourth chapter,we continue to study the geometric phase of the DQD system coupled to a QPC in the dissipative environment according to the kinematic approach of the geometric phase in the mixed states under nonunitary evolution and the Bloch-type rate equations.Furthermore,the effect of the relaxation rate on it is analyzed.We discuss further the influence and the physical mechanism of the dissipative environment on the geometric phase of the system.In the fifth chapter,we summarize the content of the previous chapters and an outlook for the next work.In the paper,the theoretical study of the geometric phase of the DQD system in these two kinds of environment expands people's understanding of the geometric phase for the different models,and provides the theoretical guidance and the experience for designing the quantum logic gates with fault tolerance by the geometric phase based on the quantum dot system in quantum information.In the meanwhile,employing the QPC as a detector to measure the geometric phase further deepens our understanding of quantum measurement.It also lays a good foundation for the development and the progress of quantum computing in the future.