开放量子系统中纠缠动力学的理论研究

发布时间：2019-03-30 14:54

【摘要】：作为量子力学、信息学以及计算机科学的多元交叉学科,量子信息学承载着人类跨越经典信息科学极限的梦想。现今它的迅猛发展也为传统的通信和计算机领域带来了深刻的变革,同时量子信息在理论和实验上的丰硕成果也丰富了量子力学的深刻内涵。众所周知,微观系统的量子性在现实条件下是极其脆弱的,其内部的相干性或者纠缠极易受到周围复杂环境的破坏,这也成为量子信息在处理和计算过程中最主要的障碍。因此抑制量子系统的退相干,保护系统的量子性具有十分重要的现实意义。从理论的角度,研究开放量子系统的动力学演化有助于我们理解系统的退相干机制。从现实的角度,环境对系统的影响不总是负面的,在某些情况下环境的记忆效应是保护系统量子性的关键因素。因此本文把关注点放在开放量子系统中的non-Markov记忆效应上,以实际物理系统精确的退相干动力学为基础,探索了一种普遍的利用环境的特殊结构来实现系统量子相干性长久保存的方法。本文首先概述了量子力学的发展史,从量子与经典的过渡问题出发论述了研究开放量子系统的必要性并简要回顾了该领域的研究现状。在第二章,我们介绍了Feynman-Vernon影响泛函理论,它是本文的理论基础。第三章开始介绍本文的主要工作,首先从有效费米子模型出发构建了玻色环境下费米系统精确的纠缠动力学,并且在此基础上构想了针对费米系统的退相干抑制方案。在第四章我们将退相干抑制方案应用到实际的物理系统中。在具有优异可集成性、可控性以及良好稳定性的量子点纳米结构中,通过求解系统严格的约化密度矩阵和分析非平衡格林函数,我们发现环境的记忆效应是产生最大稳态费米纠缠的关键。第五章我们将目光转向连续变量系统,探索non-Markov性如何影响腔光机械系统的辐射压效应。为此我们利用精确的微扰形式解有效地考虑了环境的记忆效应,将目前基于Born-Markov近似下的光机械系统的基础理论推广至non-Markov区域。在第六章通过利用Heisenberg绘景和Schrodinger绘景的等价性,我们在理论上解析地重构了x-x耦合谐振子的波函数和密度矩阵。本论文的研究对于理解纠缠在开放量子系统中的演化具有积极作用。从离散变量量子系统到连续变量量子系统,本论文的研究方法可能在更广泛的物理系统中得到应用。
[Abstract]:As a multi-discipline of quantum mechanics, informatics and computer science, quantum informatics carries the dream of crossing the limits of classical information science. Nowadays, its rapid development has brought profound changes to the traditional communication and computer fields, and the rich achievements of quantum information in theory and experiment have also enriched the profound connotation of quantum mechanics. It is well known that the quantum property of micro-system is extremely fragile in reality, and its internal coherence or entanglement is easily destroyed by the surrounding complex environment, which also becomes the most important obstacle in the processing and calculation of quantum information. Therefore, it is of great practical significance to restrain the decoherence of quantum system and protect the quantum property of the system. From the theoretical point of view, studying the dynamics evolution of the open quantum system is helpful to understand the decoherence mechanism of the system. From the point of view of reality, the influence of environment on the system is not always negative. In some cases, the memory effect of environment is the key factor to protect the quantum property of the system. Therefore, this paper focuses on the non-Markov memory effect in the open quantum system, based on the exact decoherence dynamics of the physical system. In this paper, a universal method to realize the long-term preservation of quantum coherence by using the special structure of environment is explored. In this paper, we first summarize the history of quantum mechanics, discuss the necessity of studying open quantum systems from the transition between quantum and classical problems, and briefly review the present research situation in this field. In the second chapter, we introduce the Feynman-Vernon influence functional theory, which is the theoretical basis of this paper. In chapter 3, the main work of this paper is introduced. Firstly, the exact entanglement dynamics of Fermi system in Bose environment is constructed from the effective fermion model, and then the decoherence suppression scheme for Fermi system is proposed. In chapter 4, we apply the de-coherent suppression scheme to the actual physical system. In quantum dot nanostructures with excellent integrability, controllability and good stability, by solving the strictly reduced density matrix of the system and analyzing the non-equilibrium Green's function, We find that the environmental memory effect is the key to the maximum steady-state Fermi entanglement. In chapter 5, we turn our attention to the continuous variable system to explore how the non- Markov property affects the radiation pressure effect of the cavity optical mechanical system. Therefore, the memory effect of the environment is effectively considered by the exact perturbation solution, and the basic theory of the optical mechanical system based on the Born-Markov approximation is extended to the non-Markov region. In chapter 6, we reconstruct the wave function and density matrix of the coupled harmonic oscillator analytically by using the equivalence of Heisenberg and Schrodinger pictures. The research in this paper plays a positive role in understanding the evolution of entanglement in open quantum systems. From discrete variable quantum system to continuous variable quantum system, the research method in this paper may be applied to a wider range of physical systems.
【学位授予单位】：大连理工大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O413.1

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