【作者】 楼越升；

【导师】 丛爽；

【作者基本信息】 中国科学技术大学 ， 系统工程， 2010， 博士

【摘要】 寻找有效的量子系统控制场设计方法在量子控制理论以及实践中占有关键的地位,对量子信息、量子物理、化学选键、纳米及微生物技术等领域的发展具有重要的指导意义。但是由于量子系统本身的一些特性,对一般的高维复杂量子系统的控制场设计依然是很困难的,目前还没一种普适的量子控制场的设计方法,还需要广大的科研工作者付出不懈的努力。在这一背景下,本论文重点研究了量子位系统的控制场开环设计、封闭量子系统一般混合态的量子Lyapunov设计以及开放量子系统的控制场设计等问题。具体内容包含一下几个方面：1、研究Lyapunov控制场设计技术在封闭量子系统中的应用问题。首先,利用相互作用图景变换将量子系统的动力学方程变换为齐次双线性方程,在此基础上设计Lyapunov控制律实现封闭量子系统一般混合态的控制；其次,针对目前Lyapunov方法普遍存在的收敛性问题,证明了一定条件下Lyapunov方法收敛的充分必要条件。利用量子状态的相干向量表示,设计Lyapunov函数的虚拟观测量算符,在保证控制律的稳定性的基础上,从Barblat引理出发,获得量子系统最大状态不变集的结构,通过分析最大不变集中状态的动力学稳定性,证明一定条件下量子Lyapunov方法收敛的充分必要条件；第三,针对量子系统在Lyapunov控制律作用下无法收敛到给定的目标状态的情况,利用李群分解技术对量子Lyapunov方法进行改进,提出量子跃迁路径规划策略,实现到目标状态的控制,并证明了该策略的收敛性；最后,通过数值仿真实验检验了相应的分析以及所提策略的正确性。2、针对量子位系统进行控制场设计。首先,基于单量子位系统状态的Bloch球表示,从几何的角度设计控制场实现单量子位任意纯态之间的演化；其次,对于双量子位系统,根据绝热通道技术来设计控制脉冲,并利用不同脉冲之间的相干相位来制备不同的状态,分析并总结出了相干相位与制备的状态之间的近似关系；第三,从各个基本控制脉冲的物理意义出发,根据系统控制哈密顿量与能级跃迁结构之间的关系着手,针对多量子位系统设计控制脉冲序列,实现布居数的相干转移;第四,进行系统数值仿真实验对所设计的控制场进行检验。3、研究开放量子系统控制场的设计问题。首先,从最简单的情况出发,研究外加控制场对粒子间相互作用引起的纯度以及相干性变化产生的影响,并设计控制场保持被控粒子的纯度以及消除粒子纯度的波动；第二,提出将系统粒子与辅助粒子间的相互作用作为控制手段,引入局部非幺正作用,并设计相互作用强度变化以对系统粒子的纯度和相干性进行补偿,以及抵消系统粒子的消相干过程；最后,进行系统数值仿真实验,验证了所设计控制场的有效性。4、定义了一种弱测量算符的结构,并给出其参数需要满足的充分条件。分析弱测量对不同量子系统状态演化的影响,并讨论其在开放量子系统耗散及消相干控制问题中的应用。更多还原

【Abstract】 The studies of control fields design methods for quantum systems is a critical issue in quantum control theory and practice, it can greatly promotes many developing domains such as quantum information, quantum physics, bond selective chemistry, nanometer and microbial techniques. However, due to the properties of quantum systems themselves, it is difficult to design control fields for generic high-dimension and complex quantum systems. By now, there is no universal control fields design method for quantum systems, so an untiring endeavor of the scholars in various domains is still needed. Under such a background, this thesis studies the control fields design methods for quantum systems including the open loop control design, quantum Lyapunov methods for closed quantum systems with generic mixed states, the control design for open quantum systems and so on. The main contents are as follows:1. The Lyapunov based methods for quantum systems are researched. At first, the dynamical equation of the quantum system is transferred into a homogeneous bilinear one in the interaction picture, so it becomes a homogeneous bilinear equation. Based on this, the Lyapunov control law is designed to achieve the generic mixed states control for closed quantum systems described in the interaction picture. The next, aiming at the convergence problem universally exists in the quantum Lyapunov methods at present, the sufficient and necessary conditions are proved under certain assumptions. The observable operator in the Lyapunov function is constructed using the coherent vector presentation of quantum states to guarantee the stability the control law. Based on this, the largest invariant set of the controlled system is deduced utilizing the Barblat lemma. The sufficient and necessary conditions are proved through the analyzing of the dynamical stabilities of the states in the largest invariant set. Then, for the situation that the system can’t converge to the given target state, the Lie group decomposition technology is utilized to improve the quantum Lyapunov methods, and a strategy called transition path programming is proposed to accomplish the control task, the convergence of the proposed strategy is also proved; at last, system numerical simulation experiments are done to verify the validity of the analysis and the strategy proposed.2. Control fields for cubit systems are designed. Firstly, based on the Bloch sphere presentation of a single qubit state, control fields are designed from the viewpoint of the geometry to achieve an arbitrary pure state of a single qubit. Secondly, adiabatic passage technology is used to design control fields for two-qubit systems, the coherence phase between control pulses is utilized to prepare different quantum states, the relationship between the coherence phase and the states prepared are analyzed and an approximate equation is summarized. Thirdly, utilizing the physical meanings of the basic control pulses and the relation between the system control Hamiltonians and the energy level structure, control pulse sequences are designed to accomplish the population transfer of multi-qubit systems. And fourthly, system numerical simulations are done to verify the validity of the control pulses.3. Control fields design methods for open quantum systems are studied. For the simplest case, the impact of external control fields on the purity and coherence variety due to the interaction between particles is studied, and control fields are designed to preserve the particle purity and eliminate the purity fluctuations. A new control method is proposed, in which local non-unitary operations are induced by an assistant system and its interactions with the priori system. By controlling the interactions between the two systems, the purity and coherence of the priori system are compensated, and the decoherence effect is counteracted. All the designs are verified by numerical simulation experiments.4. A kind of weak measurement operators is defined. A sufficient condition of the parameters is given. The impact of weak measurements on different quantum systems are analyzed, and the applications of such measurements in dissipation and decoherence control for open quantum systems are also discussed.更多还原