The Effect Of Bath Structure And Temperature On Dissipative Quantum Dynamics

After the establishment of the quantum mechanics, its application tophysical science has achieved great success, which leads to the invention oflaser, transistor and the development of semiconductor industry. Connect-ing the quantum world and the classical world, the quantum dissipationplays an important role in many physical and chemical processes, fromspontaneous emission to electron transfer in molecular, from quantum de-coherence to photon harvest in photosynthesis. In the context of quantumcomputation, we study the dynamics of quantum bit (qubit) with variousenvironments.Spin-boson model (SBM), the simplest possible non-trivial model inthe ?eld of quantum dissipation, can be used to describe the decoher-ence of qubit. In the past decades, a large number of in-depth studiesof SBM was done and great progress has been made, whereas, there arestill some problems related to the theoretical study of SBM. Many ana-lytical works are based on the rotating wave approximation (RWA) or theMarkov approximation, which work well only in some speci?c situations,such as on-resonance, weak-coupling or short memory time, etc. How-ever, as to the quantum computation, the most promising candidate, thesolid state qubit, always su?ers strong dissipation and the environment may have particular structure, which challenge the validity of the aboveapproximations.In this work, a perturbative method based on a unitary transfor-mation is developed, which avoids the RWA and Markov approximation,and is suitable in both weak and the strong coupling regime. By usinga polaron-like transformation, we can deal with the adiabatic and non-adiabatic bosons separately, and obtain the dissipative qubit dynamics bysolving the non-Markov master equation. In real cases, the qubit is alwaysin a structured environment, for example, the Josephson qubit su?ers theintrinsic slow noise caused by the two level ?uctuators; the ?ux qubit iscoupled to a read-out device modeled as a damped harmonic oscillator. Inthis work we mainly focus on the qubit dynamics in structrued environ-ments. And six chapters are presented.In Chapter One, we ?rst review the research history of dissipativeproblems and the background of the quantum computation. Then, the cur-rent experimental researches and the corresponding theoretical descriptionare given. Finally, we introduce the theoretical description of dissipativequantum system and the spin-boson model (SBM).In Chapter Two, we present the perturbative method based on theunitary transformation. Since the transformed Hamiltonian is similarto that of the rotating-wave approximation, we call it the transformedrotating-wave approximation (TRWA). In addition, the widely used RWAand Markov approximation methods are given and compared with theTRWA method.In Chapter Three, we study the SBM with a Lorentz structured bath,an equivalent model is a two-level system coupled to a harmonic oscilla-tor, and the later coupled to an Ohmic bath. The analytical ground state energy, the renormalized tunneling frequency and the non-Markov qubitdynamics are obtained. The results are compared to that of the numericalquasi-adiabatic path-integral (QUAPI) method and they show quantita-tive agreement. We also ?nd that, in some cases, by increasing the cou-pling between the oscillator and boson bath, the decoherence rate can bereduced. Finally, the result of RWA method is also presented, and com-pared with previous results. In the o?-resonance case, there is signi?cantdi?erence between RWA and other methods.In Chapter Four, we study the qubit dynamics in a dissipative two-level environment, the qubit is coupled to another two-level system, whichis then coupled to a boson bath. By using the TRWA method, the non-Markov dynamics of qubit is studied, and compared with the QUAPIresults. In some cases, it shows that, by increasing the coupling betweenthe two-level and the boson bath, the decoherence rate of qubit can bereduced.In Chapter Five, by using the weak coupling approximation, we studythe e?ect of temperature on the qubit dynamics under two di?erent struc-tured environments as shown in Chapter Three and Four. It shows that,when middle quantum structure is a two-level system, the qubit decoher-ence rate can be reduced or enhanced with increasing temperature ac-cording to the coupling condition; When middle structure is a harmonicoscillator, the decoherence rate can only be enhanced with temperature.In Chapter Six, the main conclusions and the prospect are given.This work was supported by the National Natural Science Founda-tion of China under contract NO. 10734020 and NO. 90503007, as well asthe National Minister of Education Program for ChangJiang Scholars andInnovative Research Team in University of IRT0524.