量子计量与量子速度极限的噪声机制的研究 Alternative Title The Noise Mechanism in Quantum Metrology and quantum speed limit 王源生 Thesis Advisor 安钧鸿 2018-04-16 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 博士 Keyword 量子计量 量子速度极限 开放量子系统 束缚态 周期驱动 Floquet 理论 Abstract 量子计量学是利用量子纠缠或压缩资源来实现超越经典物理允许精度的测量科学，在未来频标系统、微磁传感和引力波探测中具有重要应用前景；量子速度极限描述了通过微观系统参数的优化，人们所能获得的系统最快的演化时间，在量子态调控和绝热量子计算中具有基础意义。但是，微观系统普遍存在的退相干会对量子计量学和量子速度极限带来出乎意料的破坏，如何评估退相干对二者的作用并寻求恰当的方式抑制退相干对它们的影响是近年来备受关注的问题。在本文，我们将通过如下方面的研究对这些问题进行探索。 首先，我们研究了基于Ramsey干涉仪的原子频率的量子计量中的耗散噪声机制。传统对该系统的噪声分析主要集中于原子的退相位噪声，发现在玻恩-马尔科夫(Born-Markovian) 近似退相位噪声中，理想情形量子纠缠导致的频率计量精度对原子数目$n$的标度将从海森堡极限（即$n^{-1}$）退化为与经典计量散粒噪声极限相同的标准量子极限$n^{-1/2}$，说明量子优势将完全消失。在非马尔科夫( Non-Markovian) 退相位噪声中，计量精度可达到所谓的Zeno极限（即$n^{-3/4}$），该结果揭示了非马尔科夫效应对量子计量精度的建设性作用，但仅存在于利用演化进行编码的短时尺度内，在长时条件内，计量精度也同样会退化到标准量子极限，这对于量子计量的实现仍不利。本文我们对Ramsey 干涉仪中原子的耗散噪声进行了研究，我们严格的非马尔科夫耗散动力学研究发现在演化的长时尺度下，原子频率计量的误差竟然会渐进地趋于海森堡 极限，我们进一步的分析揭示这种量子计量精度提升的机制是每个原子与其环境所组成的复合系统的束缚态的形成。基于最近通过库工程来调控复合系统的能谱特性的实验进展，我们的工作提供了一种在真实实验中实现超越经典极限的量子计量的途径。 其次，我们提出了对现实条件下Ramsey量子计量的噪声进行抑制的主动控制方案— 谱过滤方法。虽然通过库工程方法调控束缚态的形成可以渐进地获得频率计量的海森堡 极限，但是一旦一个体系制备之后，就很难再进行参数调节了，这限制了库工程方法的应用。为了解决这个问题，我们分别研究了周期性外场驱动下的原子的退相位和耗散动力学，我们发现无论是退相位还是耗散，原子的退相干因子都可以表示为噪声的谱密度与周期性驱动外场的傅立叶变换的重叠积分，因此，我们可以有效的调控周期性驱动外场的参数使得该积分为零从而实现对退相位和耗散的抑制，我们将该方法命名为谱过滤法。此时在噪声Ramsey 频率计量方案中，伴随着谱过滤法导致的退相干的抑制，计量精度可以达到理想情况下海森堡极限。该结果为我们在现实条件下获得海森堡极限的量子计量提供了一个切实可行的主动调控方案。 最后，我们研究了周期性外场驱动对于开放量子系统速度极限的影响。封闭系统的量子速度极限刻画了系统从初态演化至其正交态依赖于系统参数的最短的时间，对量子计算的研制具有基础的意义。开放量子系统的速度极限刻画了在环境扰动下开放系统趋于平衡的最短时间，是衡量开放系统退相干特性的一个关键因素。以前研究发现开放系统量子加速的潜质本质上决定于其与环境形成的复合系统束缚态的形成，该结果揭示了通过库工程调控束缚态的形成来实现量子加速的方案。本文我们进一步提出利用周期性外场驱动来调控复合系统的Floquet准能谱中束缚态形成来进行量子加速的可控方案。我们发现周期驱动参数的改变可以有效地实现量子系统在可加速的与不可加速的动力学演化之间有效转变；进一步基于Floquet理论，我们分析了这些转变的产生机制，我们发现，若总系统的Floquet 准能谱中不存在束缚态，则量子速度极限时间将渐近地趋向于一个不为零的有限值，说明系统量子计算的能力有限；若总系统的准能谱中存在束缚态，则相对速度极限时间会渐近地趋于零，说明系统很强的量子加速能力。我们还进一步提出了实验验证的方案来进一步说明我们的机制。我们的研究不仅有助于实验上更灵活地实现开放系统量子加速，也对非平衡物态的研究提供了启示。 本文围绕量子工程任务中的退相干控制问题，利用束缚态理论建立了开放和周期性驱动量子系统的统一物理框架：揭示了系统和环境组成的复合系统能谱束缚态形成在现实条件下量子计量超高精度恢复中的建设性作用，揭示了周期性驱动系统的Floquet准能谱束缚态在开放系统量子加速中的积极意义。同时，本文所提出了谱过滤方法对量子计量中的噪声抑制提供了实验可行的方案 Other Abstract Quantum metrology is the study on making higher-precision measurement of physical parameters than the classically achievable one by exploiting quantum entanglement or quantum squeezing. It has diverse application prospects in future frequency standard, sensor of tiny magnetic fields, and gravitational wave detection. Quantum speed limit describes the most efficient evolution of a quantum system from an initial state to its orthogonal state, which plays a fundamental role in quantum control and adiabatic quantum computation. However, the ubiquitous decoherence in quantum world exerts unexpected detrimental influences on quantum metrology and quantum speed limit. How to evaluate the influences of decoherence on quantum metrology and quantum speed limit and how to design active ways to beat the detrimental influences of decoherence have attracted much attention in recent year. The thesis is devoted to explore these issues from the following aspects. First, we evaluate the exact impacts of local dissipative environments of each atom on quantum metrology, based on the Ramsey interferometer. The conventional study on the noise effect of such system focused on the dephasing noise. It was found that the so-called Heisenberg limit, which relates the metrology precision of the atomic frequency to the atom number as $n^{-1}$, reduces to the standard quantum limit, which scales to $n$ as $n^{-1/2}$ and is the same as the short-noise limit in classical metrology, under the Born-Markovian approximation. Further studies demonstrated that the precision raises to the so-called Zeno limit $n^{-3/4}$ when the non-Markovian effect of the local dephasing noises is considered. Although the result reveals the constructive role of the non-Markovian effect on quantum metrology, it is only present in the short-encoding-time scale and tends to vanish in the long-encoding-time condition. Our exact study on the effect of the local dissipative noises of each atom on the metrology precision indicates that the Heisenberg limit in the ideal case is asymptotically recoverable. Our analysis reveals that this is essentially due to the formation of a bound state between each atom and its environment. This provides an avenue for experimentation to implement quantum metrology under practical conditions via engineering of the formation of the system-environment bound state. Secondly, we propose an active control way, i.e., the spectrum filtering method, to suppress the effect of noise on actual quantum metrology scheme based on Ramsey interferometer. Although the Heisenberg limit is recovered asymptotically in frequency estimation scheme through reservoir engineering, the system parameters are hard to be adjusted once the system material is fabricated. This restricts the application of reservoir engineering in quantum metrology. To solve this problem, we propose a strategy to beat the dephasing and dissipative noises by periodic driving. It is found that, for both cases, the decoherence factor can be represented by an overlap integral of noise spectral density and the Fourier transform of the periodic control field. Therefore, we can make the overlap integral zero by adjusting the parameter of periodically driven field and thus the decoherence is suppressed completely. This process is what we call \textit{spectral filtering}. In the context of frequency estimation scheme based on Ramsey interferometer subjected to noise, it is capable of achieving Heisenberg limit once the decoherence is completely suppressed. This investigation supplies a feasible way in achieving Heisenberg limit under realistic condition. At last, we explore the effect of periodically driving field on quantum speed limit time of open system. The quantum speed limit time of closed system characterize the minimum time interval that quantum systems with constant energy and initial energy spread $\Delta E$ needs to evolve between two orthogonal states, which is fundamental to the research of quantum computation. Quantum speed limit time of open system reflects the minimum time that a quantum system reaches the equilibrium state under the influence of environment. It is a key factor to evaluate the decoherence properties of open quantum system. It has been pointed in previous work that the essence of potential of quantum speed up is the formation of system-reservoir bound state. This result supplies a quantum speed up scheme by using reservoir engineering. In this thesis, we go a step further and propose a quantum speedup protocol, in which a periodic driving field is applied to manipulate the formation of bound state in Floquet quasi-energy spectrum. Our result reveals that, it is possible to make the switch of open quantum system dynamics between with and without the potential of quantum speedup through adjusting parameters of periodic driving. Our further analysis demonstrates the mechanism of the switch: If the bound state does not exist in Floquet quasi-energy spectrum, the relative quantum speed limit time would approach a finite value, which implies a limited quantum speedup performance; If the bound state exists in Floquet quasi-energy spectrum, the relative quantum speed limit time would approach zero, which indicates a great potential of quantum speedup. In addition, an experimental scheme is raised to elucidate the mechanism we present above. Our research provides a flexible way to implement quantum speedup in experiment, what's more, it may also inspire the study on nonequilibrium states of matter. Concentrating on the decoherence control problem of quantum engineering schemes, we establish a unified theoretical framework of open and periodically driven quantum systems using bound state theory. The constructive role of the formation of system-reservoir bound state in completely restoring the superiority of quantum metrology under realistic condition is revealed. The positive significance of the formation of Floquet bound state in implementing quantum speedup of periodically driven open system is demonstrated. Meanwhile, we propose the spectral filtering method which supplies an experimental feasible scheme to suppress the destructive effect of decoherence on quantum metrology. URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/229600 Collection 物理科学与技术学院 Recommended CitationGB/T 7714 王源生. 量子计量与量子速度极限的噪声机制的研究[D]. 兰州. 兰州大学,2018.
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