兰州大学机构库 >物理科学与技术学院
开放系统的反常退相干效应及其经典模拟研究
Alternative TitleThe effects of anomalous decoherence in open systems and its classical simulation
马超
Thesis Advisor安钧鸿
2018-04-02
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name博士
Keyword开放量子系统 退相干 束缚态 周期驱动 量子失协
Abstract

微观系统不可避免地受到背景环境的影响而成为开放量子系统,开放量子系统动力学演化的后果是量子相干性趋于消失,该现象称作退相干。退相干既是导致物理体系从量子向经典转变的主要原因,也是实现各类量子技术任务的主要障碍。退相干的描述通常基于玻恩-马尔科夫近似,在该近似下的结果是系统相干性完全丧失。近年来开放系统的非马尔科夫退相干吸引了广泛关注,从基础研究角度,人们希望能将传统的玻恩-马尔科夫近似退相干描述的成功理论推广到非马尔科夫情形,并寻求所揭示出的新效应;另一方面,从基本应用角度,越来越多的物理体系都出现了该近似不成立的物理条件。如何认识退相干的非马尔科夫 效应及其与传统玻恩-马尔科夫近似结果的不同?我们将从以下方面对这些问题进行研究。

首先,我们分别研究了由单自旋和双自旋组成的系统在一维自旋环境中的退相干问题,各自旋之间通过XXZ耦合相互作用,该系统是磁性物理的基础,此类自旋环境导致的自旋系统的退相干也是硅基量子计算实现的主要障碍。通过严格的非马尔科夫退相干描述,我们发现自旋系统的激发动力学敏感地依赖于其与自旋环境组成的复合系统的能谱特性:若能谱中只有连续的能带,则系统自旋激发将不可逆地流失到环境自旋中,说明系统自旋发生了完全退相干,该结果与传统玻恩-马尔科夫近似的结果定性符合;若能谱中在连续能带外的能隙区还有束缚态存在,则系统自旋激发就表现出局域化,说明系统自旋的退相干被抑制,该结果与玻恩-马尔科夫近似结果具有定性的不同。我们结果说明非马尔科夫效应不仅只会在短时尺度内定量地改变系统的动力学行为,而且也会在长时极限下定性地改变系统的稳态。该反常退相干机制为我们通过操作复合系统的能谱特性来控制开放系统的退相干行为提供了一把钥匙。

其次,我们进一步探索如何利用这种反常退相干效应产生建设性的量子态制备。我们具体研究了利用此类反常退相干行为来制备连续变量由量子失协刻画的量子关联。量子失协以比量子纠缠更普遍的方式刻画了量子关联,其表现出许多奇异的性质并在许多量子信息协议中具有基础的应用。以前研究发现,不同于量子纠缠只能通过直接或间接的相互作用产生,量子失协可以由某一子系统的单局域环境产生。但是该产生的量子失协随着时间的演化和退相干的进一步发生将又退化为零,是否可以利用单局域环境产生稳定的量子失协?我们研究了仅有一个与其环境耦合的双量子光场系统的非马尔科夫退相干,利用相干态路径积分影响泛函方法建立了该开放系统严格的动力学描述,发现当光场与其局域环境组成的复合系统的能谱中只有连续能带而没有隙间束缚态时,该局域环境的确会诱导双光场产生量子失协,但随着时间演化它仍将渐进地退化至零,该结果与以前发现一致;但是只要复合系统的能谱中有隙间束缚态的形成,局域环境不仅能产生瞬时量子失协,而且还能使得该量子失协稳定地保持到其稳态。该结果为退相干辅助的量子关联制备提供了理论基础。

最后,我们在光学系统建立这种反常退相干效应的经典类比,基于此,实现了利用光在周期性调制耦合波导管阵列中的传播来模拟量子系统中的交流电场诱导的电子在晶格运动中的局域化。光学波导系统以其易制备、洁净性和可控性已成为模拟量子力学效应的基本平台,通过对光在一维周期性调制耦合波导管系统的分析,我们建立该经典系统与交流电场驱动的电子在固体晶格中运动模型的相似性,我们利用Floquet理论来处理该周期系统:Floquet本征值起着光在无调制耦合波导中传播的传播常数相同的作用,其本征态起着无调制波导阵列中的定态传播模式相同的作用。我们发现只要该光学系统的Floquet本征值谱的连续带外存在束缚传播模式,光的传播将被局域化到初始的波导管中;而当没有这种带外束缚模式时,光就不可逆地散播到环境波导阵列中。进一步分析发现我们揭示的周期性调制诱导的光局域化与传统的高频调制导致的动力学局域化不同,是光学局域传播实现的新方式。总之,我们主要揭示了在非马尔科夫退相干动力学下,复合系统束缚态的形成导致开放系统反常退相干的机制及其在量子工程任务中的积极作用;并且在相应的经典光学系统对该量子效应进行模拟,可发现此反常退相干机制具有一般普适性,这为退相干抑制提供了一种新思路。

Other Abstract

The inevitable interactions with the surrounding environment make the microscopic systems open quantum systems. The definite consequence of the nonunitary evolution of the open quantum systems is the decay of quantum coherence, i.e., the decoherence. Decoherence is the main reason of quantum-classical transition and the obstacle to the practical realization of quantum engineering schemes. The conventional Born-Markovian approximate description to the decoherence predicts the complete decay of quantum coherence. Recently, the non-Markovian decoherence has attracted wide attention. On one hand, people expect to extend the description of open quantum systems from the well-established Born-Markovian approximation regime to the general non-Markovian regime and explore the new physics that might emerge. On the other hand, with the development of experimental technique, more and more physical systems show the conditions that invalidate the Born-Markovian approximation. Therefore, how to understand the differences of non-Markovian decoherence from the conventional Born-Markovian one is a widely focused issue in quantum engineering. In this thesis, we explore this issue from the following aspects. First, we investigate the decoherence of the open system consisting of single spin and two spins interacting with the coupled spin-chain environment, respectively. The nearest spins are coupled via the XXZ interactions. On one hand, this model is the basic of quantum magnetism, on the other hand, the decoherence induced by the spin bath in such model is the main obstacle in the realization of the silicon-based quantum computation. From the established exact non-Markovian decoherence description, we find that the relaxation dynamics of the system spin sensitively depends on the character of the energy spectrum of the whole system consisting of the system and the environment. If the energy spectrum contains only a continuous energy band, the system spin relaxes to its ground state asymptotically, which characterizes a complete decoherence and coincides with the conventional Born-Markovian result. However, if a bound state is formed in the midgap area of the energy spectrum, the excitation in the system spin shows localized behavior, which characterizes decoherence suppression and cannot be found from the Born-Markovian result. Our result reveals that the non-Markovian effect can cause not only quantitative correction to the transient dynamics, but also qualitative change to the steady-state behavior to the open quantum system. This anomalous decoherence behavior supplies us an active way to control the decoherence of the open system via manipulating the energy-spectrum character of the whole system. Secondly, we proceed to explore how to use such anomalous decoherence effect to generate specific quantum states. We propose a scheme to generate stable continuous-variable quantum discord using the anomalous decoherence induced by the formation of the bound state. Quantum discord characterizes the quantum correlation in a more general manner than the quantum entanglement and has a wide application in quantum information processing. It was found that quantum discord can be induced by a local environment, which is dramatically different from quantum entanglement, which can only be generated via interactions. However, in the long-time limit, the generated quantum discord decays to zero accompanying the decoherence. Can we generate stable quantum discord via single local environment? Addressing on this problem, we investigate two quantum optical fields with only one of them interacting with a local environment. Using the path-integral influence-functional theory, we establishe the exact non-Markovian dynamics of the open system. It is found that if an optical-field-environment bound state is formed within the midgap area, the local environment can not only generate quantum discord transiently, but also can make the generated quantum discord preserved in the long-time limit. The result lays a theoretical foundation to prepare stable quantum discord by local environment. Finally, we establish a classical analog to the anomalous decoherence in optical system. We investigate the propagation of light in a coupled waveguide array with one of the waveguides periodically modulated in its geometric structure or refractive index. The light propagating in a waveguide array or photonic lattice has become an ideal platform to control light and to mimic quantum behaviors in a classical system. Within the framework of Floquet theory, it is interesting to find that the light shows the localized propagation in the modulated waveguide as long as bound quasistationary modes are formed in the band-gap area of the Floquet eigenvalue spectrum. This mechanism gives a useful instruction to confine light via engineering the periodic structure to form the bound modes. It also serves as a classical simulation of decoherence control via temporally periodic driving in open quantum systems. In summary, the thesis reveals the anomalous decoherence induced by the formation of bound state in the energy spectrum of the total system and its constructive role in quantum engineering. The classical simulation of this anomalous decoherence and its dynamical control in an optical system supplies a new idea to decoherence control.

URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/229652
Collection物理科学与技术学院
Recommended Citation
GB/T 7714
马超. 开放系统的反常退相干效应及其经典模拟研究[D]. 兰州. 兰州大学,2018.
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