小分子量子动力学性质研究
|
摘要
量子信息学是量子力学与信息科学的一门交叉学科,在最近的十几年中得到了国内外学术界的高度关注。量子计算(量子计算机)是量子信息学的重要组成部分。近年来,为了实现量子计算,科学家们提出了多种物理方案,其中之一便是用振动的分子编码量子比特实现量子计算。在这种模型中,用分子内不同的振动或转动模式来编码量子比特,用整形优化的红外激光脉冲来控制分子内不同振动或转动模式之间的能量流动,从而实现对量子比特的操控,也就是量子逻辑门的实现。这种量子计算方案与其它的一些方案相比有很多优越之处,比如,在这种方案中,由于量子比特的数目与分子的振转动自由度是成正比的,所以可实现的量子比特数目比较多；其次,分子的振转动态相对而言比较稳定,有更充足的时间完成量子计算；再次,分子的某一个振动或转动模式不只有两个本征态,可以有多个态,所以可以编码更多的量子信息。另外,在用实际的分子来模拟量子计算的理论研究中,人们已经证明使用这种计算方案可以获得极高的量子计算保真度。因此,与用振动的分子实现量子计算相关的问题成了人们近期研究的热点,例如,如何寻找合适的分子体系来完成量子计算、如何设计更高保真度的量子逻辑门、分子内部的纠缠具有什么样的特性等等。
量子纠缠作为量子世界中最神奇的特征之一,它描述了复合系统中子体系之间的非定域、非经典的关联。如果一个复合系统的量子态不能写成其子系统量子态的直积形式,就称该系统的量子态为纠缠态。纠缠是复合系统内部一种奇妙的关联,不同于经典的关联,对于有纠缠的两个系统的其中一个系统做量子操作时将影响到另一个系统。量子纠缠在复合量子系统中是普遍存在的,它与系统之间信息的传递,系统的能量耗散,量子测量等等许多问题都有联系,是目前量子物理领域特别是量子信息理论中的一个核心问题。在量子计算和量子通信领域,量子纠缠有着十分广泛的应用,例如在量子隐形传态,量子稠密编码,量子密钥分发,量子安全通信等方面。
相位是量子力学中非常重要的一个概念,它是所有干涉现象的根源,和波函数的几率幅一样有着深刻的物理意义。在早期人们研究量子力学的过程中,一直以为计算波函数的几率幅是主要任务,在波函数随时间演化的过程中,现在被称为几何相的相位被认为是一个无关紧要的物理量,可以通过规范变换将其去除掉。直到1984年,Berry在研究量子系统绝热循环演化时发现,该系统的量子态除了获得一个动力学相位外,还有一个和系统的参数的具体变化路径有关的相位,Berry就把这个相位定义为了Berry相位。随后,Simon给出了这个相位的几何解释,指出Berry相因子具有几何拓扑特征,它代表了Hermit线丛上的Holonimy,而绝热演化则自动定义了这个纤维丛上的联络。虽然几何相是在研究具体的物理系统时被发现的,但是后来的研究表明,它在量子系统中是普遍存在的,它深刻的反映了量子系统Hilbert空间的性质。后来在相应的光学实验和核磁共振实验中都证实了Berry相因子的存在。如今,对几何相的研究已经深入到数学、物理和化学等很多学科领域。
相干是量子计算机实现高效运算的基本条件之一,在实际的实施量子计算方案过程中,阻止人们实现量子计算的一个重要的障碍就是退相干,即相干性消失。退相干是由于系统和环境之间的相互作用产生的,在从理论上研究设计量子计算方案时,人们通常会把系统与环境之间的相互作用忽略掉,把系统当成一个封闭体系来考虑,但是在实际实验中,系统和环境会或多或少的发生相互作用,而这种相互作用会导致退相干,退相干带来的严重后果就是量子计算的无法完成或计算结果的准确性降低。分子振转动量子计算模型同样也会遇到退相干的问题,而这里的退相干主要是由分子与分子之间的相互碰撞或分子内部不同振转动模式或电子自由度之间的非线性耦合引起的。虽然将分子考虑在气相状态下,分子之间的碰撞可以保持在一个很低的水平,但是分子内部不同自由度之间的相互作用仍然会导致退相干,所以研究分子内的退相干机制是非常有必要的,这对于寻找无退相干的子空间以及选择合适的分子体系来完成量子计算都有很大的帮助。
量子系统区别于经典系统的另一个重要特征就是量子关联,量子纠缠是量子关联的一部分。在对多量子比特系统进行操控和测量的过程中,会引起量子比特之间很强的关联性。叠加态和纠缠态的相干性在很多量子算法,比如Shor算法中,都起到很重要的作用。多量子比特系统的相干是量子信息中重要的物理资源,为了完成量子计算,要尽可能保持长的相干性。实际上,对于一个实施量子计算或量子逻辑门操作的物理系统,完全独立于环境之外是不可能的。由于系统与环境的相互作用或子系统之间的相互作用,系统的演化不再是幺正演化,描述系统的量子态不再是纯态,而会演化到混合态。同时,制备在初始态上的相干性也会减弱或消失,这种退相干的过程对于量子计算是灾难性的。因此,理想的退相干时间要尽量比完成逻辑门操作的时间长。
量子系统的这些基本性质,如几何相、纠缠、退相干等在实施量子计算过程中都起到非常重要的作用,所以,在本篇论文中,我们将研究一下分子体系的这些性质,本文的内容安排如下：
在第一章中,我们首先给出论文的研究背景,然后介绍一下分子振转动量子计算的具体方案。接下来,我们再简单回顾一下量子系统中几何相的发展历程,最后我们将给出分子体系动力学纠缠的研究现状。
第二章中,我们将以可积二聚体为例,研究这个系统的几何相性质。对于这样一个体系,我们给出了各种初始态下几何相的解析表达式。首先研究了这个系统在局域幺正演化和非局域幺正演化下几何相的不同。然后基于一种特殊的初始态,研究了纠缠和几何相之间的动力学关系,证实了二者在一定情况下具有很好的同步性。最后,我们在系统的初始态为直积相干态的情况下,研究了总系统几何相与子系统几何相之间的关系。在这些结果中,几何相表现出了很多有趣的性质,如动力学振荡行为、单调递增行为、对称性等等。
第三章中,我们给出了一种新的代数递推方法,非常清晰的描述了双键Bose-Hubbard模型的演化规律。借助于这种方法,我们从单体纯度,能量,迹距等角度研究了双键Bose-Hubbard模型的性质,给出了这些物理量的解析表达式。通过对多种初始态下体系布居数的演化规律的研究,我们证实了随着系统参数η的变化,系统的量子态分布会发生由类约瑟夫机制到量子自陷机制的跃迁。另外,我们还考虑了玻色子之间不存在相互作用的情况,结果表明在这种条件下系统的动力学演化表现出了很好的周期性。
在第四章中,我们基于量子自陷理论,首先研究了不同类型的分子,在不同初始态下纠缠所表现出的不同性质。结果表明,将局域模分子制备在局域模初始态下更适合实现量子计算。其次,我们研究了不同类型的分子能量和纠缠之间的关系。对于不同类型的分子,能量和纠缠的关系图表现出了完全不同的物理图像。最后研究了不同类型分子内部的相干性质。这些研究都证实了分子处在低激发态时更适合完成量子计算。
在第五章中,我们主要讨论了复合量子体系内部子系统之间的初始关联和量子干涉对体系动力学性质的影响。在本章中,我们所考虑的复合量子体系为一个受外激光场驱动的耦合二能级分子体系。借助于这样一个模型体系,我们首先讨论了初始条件对单分子量子态布居数的影响。结果表明,分子间初始的关联会促进或抑制分子间的信息交流和能量交换,而初始态量子干涉的出现会进一步加强这种促进或抑制行为。另外,我们还讨论了初始条件对单分子纯度的影响。在本章的最后,我们研究了由量子态的初始相对相位引起的量子干涉对系统稳态纠缠的影响,证明了通过控制初始的相对相位可以得到任何程度的稳态纠缠。
在本篇论文的第六章,我们对前面几章的工作进行了总结,并对下一步的工作进行了展望。
Quantum information science is a cross subject of quantum mechanics and in-formation science. In the last decade, it has attracted more and more attentions in all world. Quantum computation is an important part of quantum information science. In order to realize quantum computation, in recent years, researchers have proposed many physical solutions. One of them is use the vibrational molecules to realize quantum computation. In this scheme, using the vibrational states of molecules to represent the qubits and employing a femtosecond laser pulses to im-plement quantum gate operation. This scheme has many advantages than other proposes. For example, more qubits can be realized in this scheme because the number of qubits is proportional to the number of degrees of molecular vibrational modes. In addition, the molecular vibrational state is relatively stable, so there is much more time to realize quantum computation. Moreover, the number of eigen-states of molecular vibrational mode is not only two, it may be possible to represent quantum information units having more states, then much more information can be encoded. Researches have shown that the quantum computation based on vibra-tional molecules may obtain high fidelity. Therefore, the related issues of molecular vibrational quantum computation have become popular in the recent research. Such as, how to find a more suitable molecular system to complete the quantum compu-tation, how to design a higher fidelity of quantum logic gate, what are features of quantum entanglement in molecular systems.
Quantum entanglement as one of the most important resources for quantum information processing, it describes the nonlocal, nonclassical correlation between two subsystems in a composite system. If the quantum state of a composite system cannot be written as a product state of two subsystems, the state is entangled state. Entanglement is a fantastic correlation in a composite system, it is different from the classical correlation, for one of the subsystem of quantum operation will affect the other subsystem. Quantum entanglement is a general feature in composite quan- tum system, it has relationship with the information flow, energy transfer, quantum measurement, and so on. It is a core problem in the fields of quantum informa-tion and quantum computation and it has many applications, such as in quantum teleportation, quantum dense coding, quantum key distribution, quantum secure direct communication.
Phase is a very important concept in quantum mechanics, it is the root of all quantum interference phenomena. The same to the probability amplitude, both of them have profound physical meanings. In the earlier study of quantum me-chanics, researchers always thought that calculating the probability amplitude of wave function is a major task. The so called geometric phase is not an important quantity, it can be eliminated through the gauge transformation. Until1984, in the studying of cycle adiabatic evolution of quantum system, Berry found that, except acquired a dynamical phase, the quantum state also obtain an additional phase. The additional phase is associated with the evolution path of system's parameters. This is the Berry phase. Immediately, Simon carry out the geometric interpretation of this phase, he demonstrated that the phase has geometric topology character-istic. Although the geometric phase is found in the study of specific system, in the following research, it is approved that the geometric phase exists widely in all quantum systems. It reflects the feature of Hilbert space of the system well. Later, the geometric phase was confirmed in the optical experiment and nuclear magnetic resonance experiment. Now, the study of geometric phase have permeated many fields, such as mathematics, physics and chemistry.
Coherence is one of the basic conditions for realizing quantum computation. In the implementation of quantum computation, the main obstacle in front of people is decoherence. Decoherence is generally induced by the interaction between system and environment. In the theoretical design of quantum computation scheme, the interaction between system and environment is ignored and the system is considered closed and independent. But in the experiment, the system will have interaction with environment more or less. The interaction will result in the decoherence, then the quantum computation may be not completed or the computation fidelity decreases. This situation will also appear in the molecular vibrational quantum computation. For a molecular system, the decoherence resources mainly come from the collisions with other molecules, the rotational modes or the electronic freedom-s and the intramolecular anharmonic resonances with the remaining vibrational modes. Although regarding molecules in the gas phase, the number of collisions can be kept low, studying the intramolecular decoherence mechanism is very nec-essary. This will be helpful for searching decoherence-free subspace and selecting suitable molecules to apply quantum computation.
Another important feature of quantum system different from the classical sys-tem is the quantum correlation (quantum entanglement). The operation and mea-surement on the multiqubit system will cause strong correlation between qubits. The coherence in the superposition state and entangled state play important roles in various quantum algorithms. The problem that how to maintain coherence in multiqubit system also exist. Actually, for a physical system used to implement quantum computation, it is impossible to completely independent of the environ-ment. Due to the interaction between the system and the environment or between the subsystems, the evolution of the focused system is not unitary and the state of the system is not a pure state, it will evolve into mixed state. At the same time, the coherence prepared in the initial state will weak or disappear completely. This decoherence process is disastrous for quantum computation.
So, in this thesis, based on the vibrational molecular systems, we will investi-gate some properties of molecular systems, such as geometric phase, entanglement, decoherence, and energy transfer. The thesis is organized as follows,
In chapter one, we will first give the background of our research, then make a brief introduction of using vibrational molecules to implement quantum compu-tation. In the next, we describe the development of geometric phase in quantum systems. We also review the entanglement of molecular systems in the end of this chapter.
In chapter two, we explore the dynamical properties of geometric phase for a composite quantum system under the nonlocal unitary evolution. As an illustrative example, we consider the dimer system. The analytical expressions of geometric phase under various cases are derived. We find that geometric phase presents some interesting properties with coupling strengths (corresponding to nonlocal unitary evolution), such as dynamical oscillation behavior with time evolution, monotonic-ity, symmetry, etc. In addition, we study the relationship between entanglement and geometric phase in a special case. We demonstrate that the geometric phase and entanglement have the same period for this case. Moreover, we discuss geomet-ric phase of the whole system and its subsystems in the case of the initial state of the system is product coherent state. Our investigations also show that geometric phase can reflect some inherent properties of the system:it signals a transition from self-trapping to delocalization.
In chapter three, we propose a nes algebraic recursion method to study the dy-namical evolution of the two-site Bose-Hubbard model. Actually, the two-site Bose-Hubbard mode can approximately describe the vibrations of three-atom molecules. We analyze the model's properties from the viewpoints of single partite purity, en-ergy and trace distance, in which the model is considered as a typical bipartite system. The analytical expressions for the quantities are derived. We show that the purity can well reflect the transition between different regimes for the system. In addition, we demonstrate that the transition from the delocalization regime to the self-trapping regime with the ratio η increasing not only happens for an initially local state but also for any initial states. Furthermore, we confirm that the dynam-ics of the system presents a periodicity for77=0and the period is tc=π/2J when the initial state is symmetric.
In chapter four, we study the dynamical properties of triatomic molecular sys-tems based on discrete self-trapping theory. The dynamical properties include en-tanglement of vibrations, intramolecular energy transfer and coherence. Molecules O3and SO2are employed as typical local-mode (LM) and normal-mode molecules, respectively. We demonstrated that the LM molecule prepared in a LM character-istic state is much more suitable to realize quantum computation. In addition, we investigate the relationship between entanglement and energy transfer by introduc-ing a section. The section shows completely different features for different kinds of molecules. Moreover, we study the dynamics of entanglement and energy transfer under a special condition. The both quantities reveal a good synchronism. We al-so investigate the intramolecular coherence properties by calculating the coherence visibility in the last of this chapter.
In chapter five, we mainly investigate the influences of initial correlations and quantum interference induced by a relative phase on properties of a bipartite system. The system is modeled by two two-level molecules interacting with each other via the dipole-dipole interaction and interacting with an external laser field. The properties, such as the excited state population, purity and the steady-state entanglement are studied. It is shown that the initial correlations can boost or inhibit the information flow between two subsystems during the evolution and the quantum interference will further promote this behavior. We also present an intimate relationship between the purity and the energy by introducing the Bloch sphere. Finally, the effect of the initial quantum interference on the steady-state entanglement is analyzed.
In the chapter six, we give a brief conclusion and an outlook.
量子纠缠作为量子世界中最神奇的特征之一,它描述了复合系统中子体系之间的非定域、非经典的关联。如果一个复合系统的量子态不能写成其子系统量子态的直积形式,就称该系统的量子态为纠缠态。纠缠是复合系统内部一种奇妙的关联,不同于经典的关联,对于有纠缠的两个系统的其中一个系统做量子操作时将影响到另一个系统。量子纠缠在复合量子系统中是普遍存在的,它与系统之间信息的传递,系统的能量耗散,量子测量等等许多问题都有联系,是目前量子物理领域特别是量子信息理论中的一个核心问题。在量子计算和量子通信领域,量子纠缠有着十分广泛的应用,例如在量子隐形传态,量子稠密编码,量子密钥分发,量子安全通信等方面。
相位是量子力学中非常重要的一个概念,它是所有干涉现象的根源,和波函数的几率幅一样有着深刻的物理意义。在早期人们研究量子力学的过程中,一直以为计算波函数的几率幅是主要任务,在波函数随时间演化的过程中,现在被称为几何相的相位被认为是一个无关紧要的物理量,可以通过规范变换将其去除掉。直到1984年,Berry在研究量子系统绝热循环演化时发现,该系统的量子态除了获得一个动力学相位外,还有一个和系统的参数的具体变化路径有关的相位,Berry就把这个相位定义为了Berry相位。随后,Simon给出了这个相位的几何解释,指出Berry相因子具有几何拓扑特征,它代表了Hermit线丛上的Holonimy,而绝热演化则自动定义了这个纤维丛上的联络。虽然几何相是在研究具体的物理系统时被发现的,但是后来的研究表明,它在量子系统中是普遍存在的,它深刻的反映了量子系统Hilbert空间的性质。后来在相应的光学实验和核磁共振实验中都证实了Berry相因子的存在。如今,对几何相的研究已经深入到数学、物理和化学等很多学科领域。
相干是量子计算机实现高效运算的基本条件之一,在实际的实施量子计算方案过程中,阻止人们实现量子计算的一个重要的障碍就是退相干,即相干性消失。退相干是由于系统和环境之间的相互作用产生的,在从理论上研究设计量子计算方案时,人们通常会把系统与环境之间的相互作用忽略掉,把系统当成一个封闭体系来考虑,但是在实际实验中,系统和环境会或多或少的发生相互作用,而这种相互作用会导致退相干,退相干带来的严重后果就是量子计算的无法完成或计算结果的准确性降低。分子振转动量子计算模型同样也会遇到退相干的问题,而这里的退相干主要是由分子与分子之间的相互碰撞或分子内部不同振转动模式或电子自由度之间的非线性耦合引起的。虽然将分子考虑在气相状态下,分子之间的碰撞可以保持在一个很低的水平,但是分子内部不同自由度之间的相互作用仍然会导致退相干,所以研究分子内的退相干机制是非常有必要的,这对于寻找无退相干的子空间以及选择合适的分子体系来完成量子计算都有很大的帮助。
量子系统区别于经典系统的另一个重要特征就是量子关联,量子纠缠是量子关联的一部分。在对多量子比特系统进行操控和测量的过程中,会引起量子比特之间很强的关联性。叠加态和纠缠态的相干性在很多量子算法,比如Shor算法中,都起到很重要的作用。多量子比特系统的相干是量子信息中重要的物理资源,为了完成量子计算,要尽可能保持长的相干性。实际上,对于一个实施量子计算或量子逻辑门操作的物理系统,完全独立于环境之外是不可能的。由于系统与环境的相互作用或子系统之间的相互作用,系统的演化不再是幺正演化,描述系统的量子态不再是纯态,而会演化到混合态。同时,制备在初始态上的相干性也会减弱或消失,这种退相干的过程对于量子计算是灾难性的。因此,理想的退相干时间要尽量比完成逻辑门操作的时间长。
量子系统的这些基本性质,如几何相、纠缠、退相干等在实施量子计算过程中都起到非常重要的作用,所以,在本篇论文中,我们将研究一下分子体系的这些性质,本文的内容安排如下：
在第一章中,我们首先给出论文的研究背景,然后介绍一下分子振转动量子计算的具体方案。接下来,我们再简单回顾一下量子系统中几何相的发展历程,最后我们将给出分子体系动力学纠缠的研究现状。
第二章中,我们将以可积二聚体为例,研究这个系统的几何相性质。对于这样一个体系,我们给出了各种初始态下几何相的解析表达式。首先研究了这个系统在局域幺正演化和非局域幺正演化下几何相的不同。然后基于一种特殊的初始态,研究了纠缠和几何相之间的动力学关系,证实了二者在一定情况下具有很好的同步性。最后,我们在系统的初始态为直积相干态的情况下,研究了总系统几何相与子系统几何相之间的关系。在这些结果中,几何相表现出了很多有趣的性质,如动力学振荡行为、单调递增行为、对称性等等。
第三章中,我们给出了一种新的代数递推方法,非常清晰的描述了双键Bose-Hubbard模型的演化规律。借助于这种方法,我们从单体纯度,能量,迹距等角度研究了双键Bose-Hubbard模型的性质,给出了这些物理量的解析表达式。通过对多种初始态下体系布居数的演化规律的研究,我们证实了随着系统参数η的变化,系统的量子态分布会发生由类约瑟夫机制到量子自陷机制的跃迁。另外,我们还考虑了玻色子之间不存在相互作用的情况,结果表明在这种条件下系统的动力学演化表现出了很好的周期性。
在第四章中,我们基于量子自陷理论,首先研究了不同类型的分子,在不同初始态下纠缠所表现出的不同性质。结果表明,将局域模分子制备在局域模初始态下更适合实现量子计算。其次,我们研究了不同类型的分子能量和纠缠之间的关系。对于不同类型的分子,能量和纠缠的关系图表现出了完全不同的物理图像。最后研究了不同类型分子内部的相干性质。这些研究都证实了分子处在低激发态时更适合完成量子计算。
在第五章中,我们主要讨论了复合量子体系内部子系统之间的初始关联和量子干涉对体系动力学性质的影响。在本章中,我们所考虑的复合量子体系为一个受外激光场驱动的耦合二能级分子体系。借助于这样一个模型体系,我们首先讨论了初始条件对单分子量子态布居数的影响。结果表明,分子间初始的关联会促进或抑制分子间的信息交流和能量交换,而初始态量子干涉的出现会进一步加强这种促进或抑制行为。另外,我们还讨论了初始条件对单分子纯度的影响。在本章的最后,我们研究了由量子态的初始相对相位引起的量子干涉对系统稳态纠缠的影响,证明了通过控制初始的相对相位可以得到任何程度的稳态纠缠。
在本篇论文的第六章,我们对前面几章的工作进行了总结,并对下一步的工作进行了展望。
Quantum information science is a cross subject of quantum mechanics and in-formation science. In the last decade, it has attracted more and more attentions in all world. Quantum computation is an important part of quantum information science. In order to realize quantum computation, in recent years, researchers have proposed many physical solutions. One of them is use the vibrational molecules to realize quantum computation. In this scheme, using the vibrational states of molecules to represent the qubits and employing a femtosecond laser pulses to im-plement quantum gate operation. This scheme has many advantages than other proposes. For example, more qubits can be realized in this scheme because the number of qubits is proportional to the number of degrees of molecular vibrational modes. In addition, the molecular vibrational state is relatively stable, so there is much more time to realize quantum computation. Moreover, the number of eigen-states of molecular vibrational mode is not only two, it may be possible to represent quantum information units having more states, then much more information can be encoded. Researches have shown that the quantum computation based on vibra-tional molecules may obtain high fidelity. Therefore, the related issues of molecular vibrational quantum computation have become popular in the recent research. Such as, how to find a more suitable molecular system to complete the quantum compu-tation, how to design a higher fidelity of quantum logic gate, what are features of quantum entanglement in molecular systems.
Quantum entanglement as one of the most important resources for quantum information processing, it describes the nonlocal, nonclassical correlation between two subsystems in a composite system. If the quantum state of a composite system cannot be written as a product state of two subsystems, the state is entangled state. Entanglement is a fantastic correlation in a composite system, it is different from the classical correlation, for one of the subsystem of quantum operation will affect the other subsystem. Quantum entanglement is a general feature in composite quan- tum system, it has relationship with the information flow, energy transfer, quantum measurement, and so on. It is a core problem in the fields of quantum informa-tion and quantum computation and it has many applications, such as in quantum teleportation, quantum dense coding, quantum key distribution, quantum secure direct communication.
Phase is a very important concept in quantum mechanics, it is the root of all quantum interference phenomena. The same to the probability amplitude, both of them have profound physical meanings. In the earlier study of quantum me-chanics, researchers always thought that calculating the probability amplitude of wave function is a major task. The so called geometric phase is not an important quantity, it can be eliminated through the gauge transformation. Until1984, in the studying of cycle adiabatic evolution of quantum system, Berry found that, except acquired a dynamical phase, the quantum state also obtain an additional phase. The additional phase is associated with the evolution path of system's parameters. This is the Berry phase. Immediately, Simon carry out the geometric interpretation of this phase, he demonstrated that the phase has geometric topology character-istic. Although the geometric phase is found in the study of specific system, in the following research, it is approved that the geometric phase exists widely in all quantum systems. It reflects the feature of Hilbert space of the system well. Later, the geometric phase was confirmed in the optical experiment and nuclear magnetic resonance experiment. Now, the study of geometric phase have permeated many fields, such as mathematics, physics and chemistry.
Coherence is one of the basic conditions for realizing quantum computation. In the implementation of quantum computation, the main obstacle in front of people is decoherence. Decoherence is generally induced by the interaction between system and environment. In the theoretical design of quantum computation scheme, the interaction between system and environment is ignored and the system is considered closed and independent. But in the experiment, the system will have interaction with environment more or less. The interaction will result in the decoherence, then the quantum computation may be not completed or the computation fidelity decreases. This situation will also appear in the molecular vibrational quantum computation. For a molecular system, the decoherence resources mainly come from the collisions with other molecules, the rotational modes or the electronic freedom-s and the intramolecular anharmonic resonances with the remaining vibrational modes. Although regarding molecules in the gas phase, the number of collisions can be kept low, studying the intramolecular decoherence mechanism is very nec-essary. This will be helpful for searching decoherence-free subspace and selecting suitable molecules to apply quantum computation.
Another important feature of quantum system different from the classical sys-tem is the quantum correlation (quantum entanglement). The operation and mea-surement on the multiqubit system will cause strong correlation between qubits. The coherence in the superposition state and entangled state play important roles in various quantum algorithms. The problem that how to maintain coherence in multiqubit system also exist. Actually, for a physical system used to implement quantum computation, it is impossible to completely independent of the environ-ment. Due to the interaction between the system and the environment or between the subsystems, the evolution of the focused system is not unitary and the state of the system is not a pure state, it will evolve into mixed state. At the same time, the coherence prepared in the initial state will weak or disappear completely. This decoherence process is disastrous for quantum computation.
So, in this thesis, based on the vibrational molecular systems, we will investi-gate some properties of molecular systems, such as geometric phase, entanglement, decoherence, and energy transfer. The thesis is organized as follows,
In chapter one, we will first give the background of our research, then make a brief introduction of using vibrational molecules to implement quantum compu-tation. In the next, we describe the development of geometric phase in quantum systems. We also review the entanglement of molecular systems in the end of this chapter.
In chapter two, we explore the dynamical properties of geometric phase for a composite quantum system under the nonlocal unitary evolution. As an illustrative example, we consider the dimer system. The analytical expressions of geometric phase under various cases are derived. We find that geometric phase presents some interesting properties with coupling strengths (corresponding to nonlocal unitary evolution), such as dynamical oscillation behavior with time evolution, monotonic-ity, symmetry, etc. In addition, we study the relationship between entanglement and geometric phase in a special case. We demonstrate that the geometric phase and entanglement have the same period for this case. Moreover, we discuss geomet-ric phase of the whole system and its subsystems in the case of the initial state of the system is product coherent state. Our investigations also show that geometric phase can reflect some inherent properties of the system:it signals a transition from self-trapping to delocalization.
In chapter three, we propose a nes algebraic recursion method to study the dy-namical evolution of the two-site Bose-Hubbard model. Actually, the two-site Bose-Hubbard mode can approximately describe the vibrations of three-atom molecules. We analyze the model's properties from the viewpoints of single partite purity, en-ergy and trace distance, in which the model is considered as a typical bipartite system. The analytical expressions for the quantities are derived. We show that the purity can well reflect the transition between different regimes for the system. In addition, we demonstrate that the transition from the delocalization regime to the self-trapping regime with the ratio η increasing not only happens for an initially local state but also for any initial states. Furthermore, we confirm that the dynam-ics of the system presents a periodicity for77=0and the period is tc=π/2J when the initial state is symmetric.
In chapter four, we study the dynamical properties of triatomic molecular sys-tems based on discrete self-trapping theory. The dynamical properties include en-tanglement of vibrations, intramolecular energy transfer and coherence. Molecules O3and SO2are employed as typical local-mode (LM) and normal-mode molecules, respectively. We demonstrated that the LM molecule prepared in a LM character-istic state is much more suitable to realize quantum computation. In addition, we investigate the relationship between entanglement and energy transfer by introduc-ing a section. The section shows completely different features for different kinds of molecules. Moreover, we study the dynamics of entanglement and energy transfer under a special condition. The both quantities reveal a good synchronism. We al-so investigate the intramolecular coherence properties by calculating the coherence visibility in the last of this chapter.
In chapter five, we mainly investigate the influences of initial correlations and quantum interference induced by a relative phase on properties of a bipartite system. The system is modeled by two two-level molecules interacting with each other via the dipole-dipole interaction and interacting with an external laser field. The properties, such as the excited state population, purity and the steady-state entanglement are studied. It is shown that the initial correlations can boost or inhibit the information flow between two subsystems during the evolution and the quantum interference will further promote this behavior. We also present an intimate relationship between the purity and the energy by introducing the Bloch sphere. Finally, the effect of the initial quantum interference on the steady-state entanglement is analyzed.
In the chapter six, we give a brief conclusion and an outlook.
引文
[1]R. P. Feynman. Simulating physics with computers [J]. Int. J. Theor. Phys. 1982,21:467.
[2]M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, S. Haroche. Quantum Rabi Oscillation:A Direct Test of Field Quantization in a Cavity [J]. Phys. Rev. Lett.,1996,76:1800.
[3]J. I. Cirac, P. Zoller. Quantum Computations with Cold Trapped Ions [J]. Phys. Rev. Lett.,1995,74:4091.
[4]F. Schmidt-Kaler, H. Haffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, R. Blatt. Realization of the Cirac-Zoller controlled-NOT quantum, gate [J]. Nature,2003,422:408.
[5]J. A. Jones, M. Mosca. Implementation of a quantum algorithm on a nuclear magnetic resonance quantum computer [J]. J. Chem. Phys.,1998,109:1648.
[6]R. Marx, A. F. Fahmy, J. M. Myers, W. Bermel, S. J. Glaser. Approaching five-bit NMR quantum computing [J]. Phys. Rev. A,2000,62:012310.
[7]C. Y. LU, X. Q. Zhou, O. Guhne, W. B. Gao, J. Zhang, Z. S. Yuan, A. Goebel, T. Yang, J. W. Pan. Experimental entanglement of six photons in graph states [J]. Nature Physics,2007,3:91.
[8]X. C. Yao, T. X. Wang, P. Xu, H. Lu, H. G. S. Pan, X. H. Bao, C. Z. Peng, C. Y. Lu, Y. A. Chen, J. W. Pan. Observation of eight-photon entanglement [J]. Nature Photonics,2012,6:225.
[9]J. F. Zhang, G. L. Long, Z. W. Deng, W. Z. Liu, Z. H. Lu. Nuclear magnetic resonance implementation of a quantum clock synchronization algorithm [J]. Phys. Rev. A,2004,70:062322.
[10]C. M. Tesch, L. Kurtz, R. de Vivie-Riedle. Applying optimal control theory for elements of quantum computation in molecular systems [J]. Chem. Phys. Lett. 2001,343:633.
[11]C. M. Tesch, R. de Vivie-Riedle. Quantum Computation with Vibrationally Excited Molecules [J]. Phys. Rev. Lett.,2002,89:157901.
[12]U. Troppmann, C. M. Tesch, R. de Vivie-Riedle. Preparation and addressability of molecular vibrational qubit states in the presence of anharmonic resonance [J]. Chem. Phys. Lett.,2003,378:273.
[13]J. Vala, Z. Amitay, B. Zhang. Experimental implementation of the Deutsch-Jozsa algorithm for three-qubit functions using coherent molecular superposi-tions [J]. Phys. Rev. A,2002,66:062316.
[14]S. Suzuki, K. Mishima. K. Yamashita. Ab initial study of optimal control of ammonia molecular vibrational wavepackets:Towards molecular quantum com-puting [J]. Chem. Phys. Lett.,2005,410:358.
[15]M. Y. Zhao, D. Babikov. Phase control in the vibraional qubit [J]. J. Chem. Phys.,2006,125:024105.
[16]C. Menzel-Jones, M. Shapiro. Robust operation of a universal set of logic gates for quantum computation using adiabatic population transfer between molecular levels [J]. Phys. Rev. A,2007,75:052308.
[17]K. Shioya, K. Yamashita. Quantum computing using molecular vibrational and rotational modes [J]. Mol. Phys.,2007,105:1283.
[18]M. Ndong, D. Lauvergnat, X. Chapuisat, M. Desouter-Lecomte. Optimal con-trol simulation of DJ algorithm in a two-dimensional double well coupled to an environment [J]. J. Chem. Phys.,2007,126:244505.
[19]D. Weidinger, M. Gruebele. Quantum computation with vibrationally excited polyatomic molecules:effects of rotation, level structure, and field gradients [J]. Mol. Phys.,2007,105:1999.
[20]W. S. Warren, H. Rabitz, M. Dahleh. Coherent Control of Quantum Dynamics: The Dream Is Alive [J]. Science,1993,259:1581.
[21]S. Lloyd. Coherent quantum feedback [J]. Phys. Rev. A,2000,62:022108.
[22]M. Dahleh, A. P. Peirce, H. Rabitz. Optimal control of uncertain quantum systems [J]. Phys. Rev. A,1990,42:1065.
[23]L. Zhu, V. Kleiman, X. Li, S. Lu, K. Trentelman, R. J. Gordon. Coherent Laser Control of the Product Distribution Obtained in the Photoexcitation of HI [J]. Science,1995,270:77.
[24]J. Manz, K. Sundermanna, R. de Vivie-Riedle. Quantum optimal control strate-gies for photoisom.erization via electronically excited states [J]. Chem. Phys. Lett.,1998,290:415.
[25]Y. Gu, D. Babikov. On the role of vibrational anharmonicities in a two-qubit system, [J]. J. Chem. Phys.,2009,131:034306.
[26]M. Schroder, A. Brown. Realization of the CNOT quantum gate operation in six-dimensional ammonia using the OCT-MCTDH approach [J]. J. Chem. Phys.,2009,131:034101.
[27]P. R. Zaari, A. Brown. Quantum gate operations using midinfrared binary shaped pulses on the rovibrational states of carbon monoxide [J]. J. Chem. Phys.,2010,132:014307.
[28]C. Gollub, R. de Vivie-Riedle. Modified ant-colony-optimization algorithm as an alternative to genetic algorithms [J]. Phys. Rev. A,2009,79:021401.
[29]S. Pancharatnam. Generalized Theory of Interference, and Its Applications. [J]. Proc. Indian Acad. Sci. A,1956,44:247.
[30]M. V. Berry. Quantal Phase Factors Accompanying Adiabatic Changes [J]. Proc. R. Soc. London A,1984,392:45.
[31]Y. Aharonov, J. Anandan. Phase change during a cyclic quantum evolution [J]. Phys. Rev. Lett.,1987,58:1593.
[32]J. Samuel, R. Bhandari. General Setting for Berry's Phase [J]. Phys. Rev. Lett.,1988,60:2339.
[33]A. Uhlmann. A gauge field governing parallel transport along mixed states [J]. Lett. Math. Phys.,1991.21:229.
[34]E. Sjoqvist, A. K. Pati, A. Ekert, J. S. Anandan, M. Ericsson, D. K. L. Oi, V. Vedral. Geometric Phases for Mixed States in Interferometry [J]. Phys. Rev. Lett.,2000,85:2845.
[35]D. M. Tong, E. Sjoqvist, L. C. Kwek, C. H. Oh. Kinematic Approach to the Mixed State Geometric Phase in Nonunitary Evolution [J]. Phys. Rev. Lett., 2004,93:080405.
[36]X. W. Hou, J. H. Chen, B. Hu. Entanglement and bifurcation in the integrable dimer [J]. Phys. Rev. A,2005,71:034302.
[37]X. W. Hou, M. F. Wan, Z. Q. Ma. Entropy, energy and negativity in Fermi-resonance coupled states of substituted methanes [J]. J. Phys. A:Math. Theor., 2010,43:205301.
[38]X. Hou, J. Huang. M. Wan. Vibrational spectra and tripartite entanglement in hydrogen sulfide [J]. Phys. Rev. A,2012,85:044501.
[39]Y. Liu, Y. Zheng, W. Ren, S. Ding. Dynamical entanglement of vibrations in small molecules through an analytically algebraic approach [J]. Phys. Rev. A, 2008,78:032523.
[40]L. Zhai, Y. Zheng, S. Ding. Dynamics of vibrational chaos and entanglement in triatomic molecules:Lie algebraic model [J]. Chin. Phys. B,2012,21:070503.
[41]L. Zhai. Y. Zheng. Intramolecular energy transfer, entanglement, and decoher-ence in molecular systems [J]. Phys. Rev. A,2013,88:012504.
[42]X. Meng, Y. Zheng. Entanglement, energy transfer and coherence visibility in small molecular systems [J]. J. Phys. B,2014,47:065501.
[43]H. Fujisaki. Entanglement induced by nonadiabatic chaos [J]. Phys. Rev. A, 2004,70:012313.
[44]X. W. Hou, J. Q. Chen, Z. Q. Ma. Dynamical entanglement of vibrations in an algebraic model [J]. Phys. Rev. A,2006,74:062513.
[45]X. W. Hou, M. F. Wan, Z. Q. Ma. Entropy and negativity of Fermi-resonance coupling vibrations in a spectroscopic Hamiltonian [J]. Phys. Rev. A,2009,79: 022308.
[46]M. Ericsson, A. K. Pati, E. Sjoqvist, J. Brannlund, D. K. L. Oi. Mixed State Geometric Phases, Entangled Systems, and Local Unitary Transformations [J]. Phys. Rev. Lett.,2003,91:090405.
[47]K. P. Marzlin, S. Ghose, B. C. Sanders. Geometric Phase Distributions for Open Quantum, Systems [J]. Phys. Rev. Lett.,2004,93:260402.
[48]R. S. Whitney, Y. Makhlin, A. Shnirman, Y. Gefen. Geometric Nature of the Environment-Induced Berry Phase and Geometric Dephasing [J]. Phys. Rev. Lett.,2005,94:070407.
[49]H. Goto, K. Ichimura. Geometric phase for mixed states:Formulation based on a connection on a vector bundle over a Grassmann manifold [J]. Phys. Rev. A,2007,76:012120.
[50]D. Moller, L. B. Madsen, K. Molmer, Geometric phases in open tripod systems [J]. Phys. Rev. A,2008,77:022306.
[51]X. D. Cui, Y. Zheng. Geometric phases in non-Hermitian quantum mechanics [J]. Phys. Rev. A,2012,86:064104.
[52]X. Meng, H. Feng. Y. Zheng. Dynamics of geometric phase for composite quan-tum system under nonlocal unitary transformation:a case study of dimer sys-tem [J]. Eur. Phys. J. D,2013,67:190.
[53]D. M. Tong, E. Sjoqvist, L. C. Kwek, C. H. Oh, M. Ericsson. Relation between geometric phases of entangled bipartite systems and their subsystems [J]. Phys. Rev. A,2003,68:022106.
[54]E. Sjoqvist. Geometric phase for entangled spin pairs [J]. Phys. Rev. A,2000, 62:022109.
[55]M. S. Williamson, V. Vedral. Composite geometric phase for multipartite en-tangled states [J]. Phys. Rev. A,2007,76:032115.
[56]X. X. Yi, L. C. Wang, T. Y. Zheng. Berry Phase in a Composite System [J]. Phys. Rev. Lett.,2004,92:150406.
[57]R. A. Bertlmann, K. Durstberger, Y. Hasegawa, B. C. Hiesmayr. Berry phase in entangled systems:A proposed experiment with single neutrons [J]. Phys. Rev. A,2004,69:032112.
[58]X. X. Yi, H. T. Cui, Y. H. Lin, H. S. Song. Effect of intersubsystem couplings on the evolution of composite systems [J]. Phys. Rev. A,2005,71:022107.
[59]B. Basu. Relation between concurrence and Berry phase of an entangled state of two spin-(1/2) particles [J]. Europhys. Lett.,2006,73:833.
[60]P. Milman. Phase dynamics of entangled qubits [J]. Phys. Rev. A,2006,73: 062118.
[61]C. E. R. Souza, J. A. O. Huguenin, P. Milman, A. Z. Khoury. Topological Phase for Spin-Orbit Transformations on a Laser Beam [J]. Phys. Rev. Lett.,2007, 99:160401.
[62]S. Sponar, J. Klepp, R. Loidl, S. Filipp, K. Durstberger-Rennhofer, R. A. Bertlmann, G. Badurek, H. Rauch. Y. Hasegawa. Geometric phase in entangled systems:A single-neutron interferometer experiment [J]. Phys. Rev. A,2010, 81:042113.
[63]C. W. Niu, G. F. Xu, L. Liu, L. Kang, D. M. Tong, L. C. Kwek. Separable states and geometric phases of an interacting two-spin system [J]. Phys. Rev. A,2010,81:012116.
[64]C. S. Castro, M. S. Sarandy. Entanglement dynamics via geometric phases in quantum spin chains [J]. Phys. Rev. A,2011,83:042334.
[65]C. Orzel, A. K. Tuchman, M. L. Fenselau, M. Yasuda, M. A. Kasevich. Squeezed States in a Bose-Einstein Condensate [J]. Science,2001,291:2386.
[66]M. E. Kellman, V. Tyng. Bifurcation effects in coupled Bose-Einstein conden-sates [J]. Phys. Rev. A,2002,66:013602.
[67]L. Sanz, R. M. Angelo, K. Furuya. Entanglement dynamics in a two-mode nonlinear bosonic Hamiltonian [J]. J. Phys. A,2003,36:9737.
[68]Z. Li, L. Xiao, M. E. Kellman. Phase space bifurcation structure and the gener-alized local-to-normal transition in resonantly coupled vibrations [J]. J. Chem. Phys.,1990,92:2251.
[69]T. Sako, K. Yamanouchi, F. Iachello. Classical-limit analysis of the normal-to-local transition by the algebraic effective Hamiltonian approach [J]. J. Chem. Phys.,2001,114:9441.
[70]S. Aubry, S. Flach, K. Kladko, E. Olbrich. Manifestation of Classical Bifurca-tion in the Spectrum of the Integrable Quantum Dimer [J]. Phys. Rev. Lett., 1996,76:1607.
[71]B. Xiong, J. Gong, H. Pu, W. Bao, B. Li. Symmetry breaking and self-trapping of a dipolar Bose-Einstein condensate in a double-well potential [J]. Phys. Rev. A,2009,79:013626.
[72]R. Bhandari. SU(2) phase jumps and geometric phases [J]. Phys. Lett. A,1991, 157:221.
[73]N. Mukunda, R. Simon. Quantum Kinematic Approach to the Geometric Phase. [J]. Ann. Phys. (NY).1993,228:205.
[74]A. Tipsmark, R. Dong, A. Laghaout, P. Marek, M. Jezek, U. L. Andersen. Experimental demonstration of a Hadamard gate for coherent state qubits [J]. Phys. Rev. A,2011,84:050301.
[75]A. K. Pati. Geometric aspects of noncyclic quantum evolutions [J]. Phys. Rev. A,1995,52:2576.
[76]L. E. Oxman, A. Z. Khoury. Fractional Topological Phase for Entangled Qudits [J]. Phys. Rev. Lett.,2011,106:240503.
[77]S. Zollner, H. D. Meyer, P. Schmelcher. Few-Boson Dynamics in Double Wells: From Single-Atom to Correlated Pair Tunneling [J]. Phys. Rev. Lett.,2008, 100:040401.
[78]M. P. A. Fisher, P. B. Weichman, G. Grinstein, D. S. Fisher. Boson localization and the superfluid-insulator transition [J]. Phys. Rev. B,1989,40:546.
[79]T. D. Kuhner, H. Monien. Phases of the one-dimensional Bose-Hubbard model [J]. Phys. Rev. B,1998,58:R14741.
[80]O. Romero-Isart, K. Eckert, C. Rodo, A. Sanpera. Transport and entanglement generation in the Bose-Hubbard model [J]. J. Phys. A,2007,40:8019.
[81]A. Tomadin, R. Mannella, S. Wimberger. Many-Body Interband Tunneling as a Witness of Complex Dynamics in the Bose-Hubbard Model [J]. Phys. Rev. Lett.,2007,98:130402.
[82]U. Bissbort, F. Deuretzbacher, W. Hofstetter. Effective multibody-induced tun-neling and interactions in the Bose-Hubbard model of the lowest dressed band of an optical lattice [J]. Phys. Rev. A,2012,86:023617.
[83]D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, P. Zoller. Cold Bosonic Atoms in Optical Lattices [J]. Phys. Rev. Lett.,1998,81:3108.
[84]P. Anders, E. Gull, L. Pollet, M. Troyer, P. Werner. Dynamical Mean Field Solution of the Bose-Hubbard Model [J]. Phys. Rev. Lett.,2010,105:096402.
[85]C. Trefzger, K. Sengupta. Nonequilibrium Dynamics of the Bose-Hubbard Mod-el:A Projection-Operator Approach [J]. Phys. Rev. Lett.,2011,106:095702.
[86]B. L. Chen, S. P. Kou, Y. Zhang, S. Chen. Quantum phases of the Bose-Hubbard model in optical superlattices [J]. Phys. Rev. A,2010,81:053608.
[87]K. Sakmann, A. I. Streltsov,0. E. Alon, L. S. Cederbaum. Quantum dynamics of attractive versus repulsive bosonic Josephson junctions:Bose-Hubbard and full-Hamiltonian results [J]. Phys. Rev. A,2010,82:013620.
[88]M. Collura, H. Aufderheide, G. Roux, D. Karevski. Entangling many-body bound states with propagative modes in Bose-Hubbard systems [J]. Phys. Rev. A,2012,86:013615.
[89]M. Pino, J. Prior. A. M. Somoza, D. Jaksch, S. R. Clark. Reentrance and entanglement in the one-dimensional Bose-Hubbard model [J]. Phys. Rev. A, 2012,86:023631.
[90]K. Ziegler. Dynamics of two-site Fermi-Hubbard and Bose-Hubbard systems [J]. Phys. Rev. A,2010,81:034701.
[91]S. Longhi. Optical realization of the two-site Bose-Hubbard model in waveguide lattices [J]. J. Phys. B,2011,44:051001.
[92]M. Mele-Messeguer, B. Julia-Diaz, A. Polls. Improved Variational Approach to the Two-Site Bose-Hubbard Model [J]. J. Low. Temp. Phys.,2011,165:180.
[93]G. Mazzarella, L. Salasnich, A. Parola, F. Toigo. Coherence and entangle-ment in the ground state of a bosonic Josephson junction:From macroscopic Schrodinger cat states to separable Fock states [J]. Phys. Rev. A,2011,83: 053607.
[94]L. Dell'Anna. Analytical approach to the two-site Bose-Hubbard model:From Fock states to Schrodinger cat states and entanglement entropy [J]. Phys. Rev. A,2012,85:053608.
[95]M. Greiner, O. Mandel, T. Esslinger, T. W. Hansch, I. Bloch. Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms [J]. Nature.2002,415:39.
[96]P. Buonsante, A. Vezzani. Ground-State Fidelity and Bipartite Entanglement in the Bose-Hubbard Model [J]. Phys. Rev. Lett.,2007,98:110601.
[97]X. Deng, L. Santos. Entanglement spectrum of one-dimensional extended Bose-Hubbard models [J]. Phys. Rev. B,2011,84:085138.
[98]K. K. Xg, Y. C. Chen, Y. C. Tzeng. Quarter-filled supersolid and solid phases in the extended Bose-Hubbard model [J]. J. Phys.:Condens. Matter,2010.22: 185601.
[99]M. S. Underwood, D. L. Feder. Bose-Hubbard model for universal quantum-walk-based computation [J]. Phys. Rev. A,2012,85:052314.
[100]M. Oktel, M. Nit;a, B. Tanatar. Mean-field theory for Bose-Hubbard m.odel under a magnetic field [J]. Phys. Rev. B,2007,73:045133.
[101]S. Ejima, H. Fehske, F. Gebhard. Dynamic properties of the one-dimensional Bose-Hubbard model [J]. Europhys. Lett.,2011,93:30002.
[102]D. Rossini, R. Fazio. Phase diagram of the extended Bose-Hubbard model [J]. New J. Phys.,2012,14:065012.
[103]J. M. Zhang. R. X. Dong. Exact diagonalization:the Bose-Hubbard model as an example [J]. Eur. J. Phys.,2010,31:591.
[104]L. Wang, Y. Hao, S. Chen. Quantum dynamics of repulsively bound atom pairs in the Bose-Hubbard model [J]. Eur. Phys. J. D,2008,48:229.
[105]N. Teichmann, D. Hinrichs, M. Holthaus. Process-chain approach to the Bose-Hubbard model:Ground-state properties and phase diagram [J]. Phys. Rev. B, 2009,79:224515.
[106]G. Mazzarella, M. Moratti, L. Salasnich, F. Toigo. Nonlinear quantum model for atomic Josephson junctions with one and two bosonic species [J]. J. Phys. B,2010,43:065303.
[107]H. P. Breuer, E. M. Laine, J. Piilo. Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems [J]. Phys. Rev. Lett.,2009, 103:210401.
[108]E. M. Laine, J. Piilo. H. P. Breuer. Measure for the non-Markovianity of quantum processes [J]. Phys. Rev. A,2010,81:062115.
[109]B. Julia-Diaz, D. Dagnino, M. Lewenstein, J. Martorell. A. Polls. Macroscopic self-trapping in Bose-Einstein condensates:Analysis of a dynamical quantum phase transition [J]. Phys. Rev. A,2010,81:023615.
[110]T. Yu. Entanglement decay versus energy change:A m.odel [J]. Phys. Lett. A, 2007,361:287.
[111]C. Gollub, U. Troppmann, R. de Vivie-Riedle. The role of anharmonicity and coupling in quantum computing based on vibrational qubits [J]. New J. Phys., 2006,8:48.
[112]C. M. Tesch, R. de Vivie-Riedle R Vibrational molecular quantum comput-ing:Basis set independence and theoretical realization of the Deutsch-Jozsa algorithm [J]. J. Chem. Phys.,2004,121:12158.
[113]B. M. R. Korff, U. Troppmann, K. L. Kompa. R. de Vivie-Riedle. Manganese pentacarbonyl bromide as candidate for a molecular qubit system operated in the infrared regime [J]. J. Chem. Phys.,2005,123:244509.
[114]U. Troppmann, C. Gollub, R. de Vivie-Riedle. The role of phases and their interplay in molecular vibrational quantum computing with multiple qubits [J]. New J. Phys.,2006,8:100.
[115]W. Zhu, J. Botina, H Rabitz. Rapidly convergent iteration methods for quan-tum optimal control of population [J]. J. Chem. Phys.,1998,108:1953.
[116]Y. Ohtsuki, W. Zhu, H. Rabitz. Monotonically convergent algorithm for quan-tum optimal control with dissipation [J]. J. Chem. Phys.,1999,110:9825.
[117]J. P. Palao, R. Kosloff. Optimal control theory for unitary transformations [J]. Phys. Rev. A,2003,68:062308.
[118]K. Mishima, K. Yamsshita. Decoherence of intramolecular vibrational entan-glement in polyatomic molecules [J]. Int. J. Quantum Chem.,2009,109:1827.
[119]M. C. Tichy. F. Mintert, A. Buchleitner. Essential entanglement for atomic and molecular physics [J]. J. Phys. B,2011,44:192001.
[120]T. Yu, J. H. Eberly. Sudden Death of Entanglement [J]. Science,2009,323: 598.
[121]A. C. Scott, J. C. Eilbeck. The quantized discrete self-trapping equation [J]. Phys. Lett. A,1986,119:60.
[122]S. Bose:V. Vedral. Mixedness and teleportation [J]. Phys. Rev. A,2000,61: 040101.
[123]F. Iachello, R. D. Levine. Algebraic Theory of Molecules [M]. New Youk: Oxford University Press,1995.
[124]Z. Xu, Y. Gao, Calculation of vibrational spectroscopy for tri-atomic molecules using interaction model [J]. Acta Phys.-Chim. Sin.,1996,12:555.
[125]J. Gambetta, A. Blais, D. I. Schuster, A. Wallraff, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, R. J. Schoelkopf. Qubit-photon interactions in a cavity: Measurement-induced dephasing and number splitting [J]. Phys. Rev. A,2006, 74:042318.
[126]M. Yonac, T. Yu, J. H. Eberly. Pairunse concurrence dynamics:a four-qubit model [J]. J. Phys. B,2007,40:s45.
[127]K. Kraus. States, Effects, and Operations [M]. Berlin:Springer,1983.
[128]M. A. Nielsen and I. L. Chuang Quantum Compuation and Quantum Infor-mation [M]. Cambridge:Cambridge University Press,2000.
[129]R. Alicki, K. Lendi. Quantum Dynamical Semigroups and Applications [M]. Berlin:Springer,2007.
[130]T. F. Jordan, A. Shaji, E. C. G. Sudarshan. Dynamics of initially entangled open quantum systems [J]. Phys. Rev. A,2004,70:052110.
[131]H. A. Carteret, D. R. Terno, K. Zyczkowski. Dynamics beyond completely positive maps:Some properties and applications [J]. Phys. Rev. A,2008,77: 042113.
[132]A. Shabani, D. A. Lidar. Vanishing Quantum Discord is Necessary and Suf-ficient for Completely Positive Maps [J]. Phys. Rev. Lett.,2009,102:100402.
[133]C.-F. Li, J.-S. Tang, Y.-L. Li, G.-C. Guo. Experimentally witnessing the initial correlation between an open quantum system and its environment [J]. Phys. Rev. A.2011,83:064102.
[134]A. Smirne, D. Brivio, S. Cialdi, B. Vacchini, M. G. A. Paris. Experimen-tal investigation of initial system-environment correlations via trace-distance evolution [J]. Phys. Rev. A,2011,84:032112.
[135]G. V. Varada, G. S. Agarwal. Two-photon resonance induced by the dipole-dipole interaction [J]. Phys. Rev. A,1992,45:6721.
[136]C. Hettich, C. Schmitt, J. Zitzmann, S. Kuhn, I. Gerhardt, V. Sandoghdar. Nanometer Resolution and Coherent Optical Dipole Coupling of Two Individual Molecules [J]. Science,2002,298:385.
[137]J. H. Reina, R. G. Beausoleil, T. P. Spiller, W. J. Munro. Radiative Correc-tions and Quantum Gates in Molecular Systems [J]. Phys. Rev. Lett.,2004, 93:250501.
[138]D. Z. Rossatto, T. Werlang, L. K. Castelano, C. J. Villas-Boas, F. F. Fanchini. Purity as a witness for initial system-environment correlations in open-system dynamics [J]. Phys. Rev. A,2011,84:042113.
[2]M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, S. Haroche. Quantum Rabi Oscillation:A Direct Test of Field Quantization in a Cavity [J]. Phys. Rev. Lett.,1996,76:1800.
[3]J. I. Cirac, P. Zoller. Quantum Computations with Cold Trapped Ions [J]. Phys. Rev. Lett.,1995,74:4091.
[4]F. Schmidt-Kaler, H. Haffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, R. Blatt. Realization of the Cirac-Zoller controlled-NOT quantum, gate [J]. Nature,2003,422:408.
[5]J. A. Jones, M. Mosca. Implementation of a quantum algorithm on a nuclear magnetic resonance quantum computer [J]. J. Chem. Phys.,1998,109:1648.
[6]R. Marx, A. F. Fahmy, J. M. Myers, W. Bermel, S. J. Glaser. Approaching five-bit NMR quantum computing [J]. Phys. Rev. A,2000,62:012310.
[7]C. Y. LU, X. Q. Zhou, O. Guhne, W. B. Gao, J. Zhang, Z. S. Yuan, A. Goebel, T. Yang, J. W. Pan. Experimental entanglement of six photons in graph states [J]. Nature Physics,2007,3:91.
[8]X. C. Yao, T. X. Wang, P. Xu, H. Lu, H. G. S. Pan, X. H. Bao, C. Z. Peng, C. Y. Lu, Y. A. Chen, J. W. Pan. Observation of eight-photon entanglement [J]. Nature Photonics,2012,6:225.
[9]J. F. Zhang, G. L. Long, Z. W. Deng, W. Z. Liu, Z. H. Lu. Nuclear magnetic resonance implementation of a quantum clock synchronization algorithm [J]. Phys. Rev. A,2004,70:062322.
[10]C. M. Tesch, L. Kurtz, R. de Vivie-Riedle. Applying optimal control theory for elements of quantum computation in molecular systems [J]. Chem. Phys. Lett. 2001,343:633.
[11]C. M. Tesch, R. de Vivie-Riedle. Quantum Computation with Vibrationally Excited Molecules [J]. Phys. Rev. Lett.,2002,89:157901.
[12]U. Troppmann, C. M. Tesch, R. de Vivie-Riedle. Preparation and addressability of molecular vibrational qubit states in the presence of anharmonic resonance [J]. Chem. Phys. Lett.,2003,378:273.
[13]J. Vala, Z. Amitay, B. Zhang. Experimental implementation of the Deutsch-Jozsa algorithm for three-qubit functions using coherent molecular superposi-tions [J]. Phys. Rev. A,2002,66:062316.
[14]S. Suzuki, K. Mishima. K. Yamashita. Ab initial study of optimal control of ammonia molecular vibrational wavepackets:Towards molecular quantum com-puting [J]. Chem. Phys. Lett.,2005,410:358.
[15]M. Y. Zhao, D. Babikov. Phase control in the vibraional qubit [J]. J. Chem. Phys.,2006,125:024105.
[16]C. Menzel-Jones, M. Shapiro. Robust operation of a universal set of logic gates for quantum computation using adiabatic population transfer between molecular levels [J]. Phys. Rev. A,2007,75:052308.
[17]K. Shioya, K. Yamashita. Quantum computing using molecular vibrational and rotational modes [J]. Mol. Phys.,2007,105:1283.
[18]M. Ndong, D. Lauvergnat, X. Chapuisat, M. Desouter-Lecomte. Optimal con-trol simulation of DJ algorithm in a two-dimensional double well coupled to an environment [J]. J. Chem. Phys.,2007,126:244505.
[19]D. Weidinger, M. Gruebele. Quantum computation with vibrationally excited polyatomic molecules:effects of rotation, level structure, and field gradients [J]. Mol. Phys.,2007,105:1999.
[20]W. S. Warren, H. Rabitz, M. Dahleh. Coherent Control of Quantum Dynamics: The Dream Is Alive [J]. Science,1993,259:1581.
[21]S. Lloyd. Coherent quantum feedback [J]. Phys. Rev. A,2000,62:022108.
[22]M. Dahleh, A. P. Peirce, H. Rabitz. Optimal control of uncertain quantum systems [J]. Phys. Rev. A,1990,42:1065.
[23]L. Zhu, V. Kleiman, X. Li, S. Lu, K. Trentelman, R. J. Gordon. Coherent Laser Control of the Product Distribution Obtained in the Photoexcitation of HI [J]. Science,1995,270:77.
[24]J. Manz, K. Sundermanna, R. de Vivie-Riedle. Quantum optimal control strate-gies for photoisom.erization via electronically excited states [J]. Chem. Phys. Lett.,1998,290:415.
[25]Y. Gu, D. Babikov. On the role of vibrational anharmonicities in a two-qubit system, [J]. J. Chem. Phys.,2009,131:034306.
[26]M. Schroder, A. Brown. Realization of the CNOT quantum gate operation in six-dimensional ammonia using the OCT-MCTDH approach [J]. J. Chem. Phys.,2009,131:034101.
[27]P. R. Zaari, A. Brown. Quantum gate operations using midinfrared binary shaped pulses on the rovibrational states of carbon monoxide [J]. J. Chem. Phys.,2010,132:014307.
[28]C. Gollub, R. de Vivie-Riedle. Modified ant-colony-optimization algorithm as an alternative to genetic algorithms [J]. Phys. Rev. A,2009,79:021401.
[29]S. Pancharatnam. Generalized Theory of Interference, and Its Applications. [J]. Proc. Indian Acad. Sci. A,1956,44:247.
[30]M. V. Berry. Quantal Phase Factors Accompanying Adiabatic Changes [J]. Proc. R. Soc. London A,1984,392:45.
[31]Y. Aharonov, J. Anandan. Phase change during a cyclic quantum evolution [J]. Phys. Rev. Lett.,1987,58:1593.
[32]J. Samuel, R. Bhandari. General Setting for Berry's Phase [J]. Phys. Rev. Lett.,1988,60:2339.
[33]A. Uhlmann. A gauge field governing parallel transport along mixed states [J]. Lett. Math. Phys.,1991.21:229.
[34]E. Sjoqvist, A. K. Pati, A. Ekert, J. S. Anandan, M. Ericsson, D. K. L. Oi, V. Vedral. Geometric Phases for Mixed States in Interferometry [J]. Phys. Rev. Lett.,2000,85:2845.
[35]D. M. Tong, E. Sjoqvist, L. C. Kwek, C. H. Oh. Kinematic Approach to the Mixed State Geometric Phase in Nonunitary Evolution [J]. Phys. Rev. Lett., 2004,93:080405.
[36]X. W. Hou, J. H. Chen, B. Hu. Entanglement and bifurcation in the integrable dimer [J]. Phys. Rev. A,2005,71:034302.
[37]X. W. Hou, M. F. Wan, Z. Q. Ma. Entropy, energy and negativity in Fermi-resonance coupled states of substituted methanes [J]. J. Phys. A:Math. Theor., 2010,43:205301.
[38]X. Hou, J. Huang. M. Wan. Vibrational spectra and tripartite entanglement in hydrogen sulfide [J]. Phys. Rev. A,2012,85:044501.
[39]Y. Liu, Y. Zheng, W. Ren, S. Ding. Dynamical entanglement of vibrations in small molecules through an analytically algebraic approach [J]. Phys. Rev. A, 2008,78:032523.
[40]L. Zhai, Y. Zheng, S. Ding. Dynamics of vibrational chaos and entanglement in triatomic molecules:Lie algebraic model [J]. Chin. Phys. B,2012,21:070503.
[41]L. Zhai. Y. Zheng. Intramolecular energy transfer, entanglement, and decoher-ence in molecular systems [J]. Phys. Rev. A,2013,88:012504.
[42]X. Meng, Y. Zheng. Entanglement, energy transfer and coherence visibility in small molecular systems [J]. J. Phys. B,2014,47:065501.
[43]H. Fujisaki. Entanglement induced by nonadiabatic chaos [J]. Phys. Rev. A, 2004,70:012313.
[44]X. W. Hou, J. Q. Chen, Z. Q. Ma. Dynamical entanglement of vibrations in an algebraic model [J]. Phys. Rev. A,2006,74:062513.
[45]X. W. Hou, M. F. Wan, Z. Q. Ma. Entropy and negativity of Fermi-resonance coupling vibrations in a spectroscopic Hamiltonian [J]. Phys. Rev. A,2009,79: 022308.
[46]M. Ericsson, A. K. Pati, E. Sjoqvist, J. Brannlund, D. K. L. Oi. Mixed State Geometric Phases, Entangled Systems, and Local Unitary Transformations [J]. Phys. Rev. Lett.,2003,91:090405.
[47]K. P. Marzlin, S. Ghose, B. C. Sanders. Geometric Phase Distributions for Open Quantum, Systems [J]. Phys. Rev. Lett.,2004,93:260402.
[48]R. S. Whitney, Y. Makhlin, A. Shnirman, Y. Gefen. Geometric Nature of the Environment-Induced Berry Phase and Geometric Dephasing [J]. Phys. Rev. Lett.,2005,94:070407.
[49]H. Goto, K. Ichimura. Geometric phase for mixed states:Formulation based on a connection on a vector bundle over a Grassmann manifold [J]. Phys. Rev. A,2007,76:012120.
[50]D. Moller, L. B. Madsen, K. Molmer, Geometric phases in open tripod systems [J]. Phys. Rev. A,2008,77:022306.
[51]X. D. Cui, Y. Zheng. Geometric phases in non-Hermitian quantum mechanics [J]. Phys. Rev. A,2012,86:064104.
[52]X. Meng, H. Feng. Y. Zheng. Dynamics of geometric phase for composite quan-tum system under nonlocal unitary transformation:a case study of dimer sys-tem [J]. Eur. Phys. J. D,2013,67:190.
[53]D. M. Tong, E. Sjoqvist, L. C. Kwek, C. H. Oh, M. Ericsson. Relation between geometric phases of entangled bipartite systems and their subsystems [J]. Phys. Rev. A,2003,68:022106.
[54]E. Sjoqvist. Geometric phase for entangled spin pairs [J]. Phys. Rev. A,2000, 62:022109.
[55]M. S. Williamson, V. Vedral. Composite geometric phase for multipartite en-tangled states [J]. Phys. Rev. A,2007,76:032115.
[56]X. X. Yi, L. C. Wang, T. Y. Zheng. Berry Phase in a Composite System [J]. Phys. Rev. Lett.,2004,92:150406.
[57]R. A. Bertlmann, K. Durstberger, Y. Hasegawa, B. C. Hiesmayr. Berry phase in entangled systems:A proposed experiment with single neutrons [J]. Phys. Rev. A,2004,69:032112.
[58]X. X. Yi, H. T. Cui, Y. H. Lin, H. S. Song. Effect of intersubsystem couplings on the evolution of composite systems [J]. Phys. Rev. A,2005,71:022107.
[59]B. Basu. Relation between concurrence and Berry phase of an entangled state of two spin-(1/2) particles [J]. Europhys. Lett.,2006,73:833.
[60]P. Milman. Phase dynamics of entangled qubits [J]. Phys. Rev. A,2006,73: 062118.
[61]C. E. R. Souza, J. A. O. Huguenin, P. Milman, A. Z. Khoury. Topological Phase for Spin-Orbit Transformations on a Laser Beam [J]. Phys. Rev. Lett.,2007, 99:160401.
[62]S. Sponar, J. Klepp, R. Loidl, S. Filipp, K. Durstberger-Rennhofer, R. A. Bertlmann, G. Badurek, H. Rauch. Y. Hasegawa. Geometric phase in entangled systems:A single-neutron interferometer experiment [J]. Phys. Rev. A,2010, 81:042113.
[63]C. W. Niu, G. F. Xu, L. Liu, L. Kang, D. M. Tong, L. C. Kwek. Separable states and geometric phases of an interacting two-spin system [J]. Phys. Rev. A,2010,81:012116.
[64]C. S. Castro, M. S. Sarandy. Entanglement dynamics via geometric phases in quantum spin chains [J]. Phys. Rev. A,2011,83:042334.
[65]C. Orzel, A. K. Tuchman, M. L. Fenselau, M. Yasuda, M. A. Kasevich. Squeezed States in a Bose-Einstein Condensate [J]. Science,2001,291:2386.
[66]M. E. Kellman, V. Tyng. Bifurcation effects in coupled Bose-Einstein conden-sates [J]. Phys. Rev. A,2002,66:013602.
[67]L. Sanz, R. M. Angelo, K. Furuya. Entanglement dynamics in a two-mode nonlinear bosonic Hamiltonian [J]. J. Phys. A,2003,36:9737.
[68]Z. Li, L. Xiao, M. E. Kellman. Phase space bifurcation structure and the gener-alized local-to-normal transition in resonantly coupled vibrations [J]. J. Chem. Phys.,1990,92:2251.
[69]T. Sako, K. Yamanouchi, F. Iachello. Classical-limit analysis of the normal-to-local transition by the algebraic effective Hamiltonian approach [J]. J. Chem. Phys.,2001,114:9441.
[70]S. Aubry, S. Flach, K. Kladko, E. Olbrich. Manifestation of Classical Bifurca-tion in the Spectrum of the Integrable Quantum Dimer [J]. Phys. Rev. Lett., 1996,76:1607.
[71]B. Xiong, J. Gong, H. Pu, W. Bao, B. Li. Symmetry breaking and self-trapping of a dipolar Bose-Einstein condensate in a double-well potential [J]. Phys. Rev. A,2009,79:013626.
[72]R. Bhandari. SU(2) phase jumps and geometric phases [J]. Phys. Lett. A,1991, 157:221.
[73]N. Mukunda, R. Simon. Quantum Kinematic Approach to the Geometric Phase. [J]. Ann. Phys. (NY).1993,228:205.
[74]A. Tipsmark, R. Dong, A. Laghaout, P. Marek, M. Jezek, U. L. Andersen. Experimental demonstration of a Hadamard gate for coherent state qubits [J]. Phys. Rev. A,2011,84:050301.
[75]A. K. Pati. Geometric aspects of noncyclic quantum evolutions [J]. Phys. Rev. A,1995,52:2576.
[76]L. E. Oxman, A. Z. Khoury. Fractional Topological Phase for Entangled Qudits [J]. Phys. Rev. Lett.,2011,106:240503.
[77]S. Zollner, H. D. Meyer, P. Schmelcher. Few-Boson Dynamics in Double Wells: From Single-Atom to Correlated Pair Tunneling [J]. Phys. Rev. Lett.,2008, 100:040401.
[78]M. P. A. Fisher, P. B. Weichman, G. Grinstein, D. S. Fisher. Boson localization and the superfluid-insulator transition [J]. Phys. Rev. B,1989,40:546.
[79]T. D. Kuhner, H. Monien. Phases of the one-dimensional Bose-Hubbard model [J]. Phys. Rev. B,1998,58:R14741.
[80]O. Romero-Isart, K. Eckert, C. Rodo, A. Sanpera. Transport and entanglement generation in the Bose-Hubbard model [J]. J. Phys. A,2007,40:8019.
[81]A. Tomadin, R. Mannella, S. Wimberger. Many-Body Interband Tunneling as a Witness of Complex Dynamics in the Bose-Hubbard Model [J]. Phys. Rev. Lett.,2007,98:130402.
[82]U. Bissbort, F. Deuretzbacher, W. Hofstetter. Effective multibody-induced tun-neling and interactions in the Bose-Hubbard model of the lowest dressed band of an optical lattice [J]. Phys. Rev. A,2012,86:023617.
[83]D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, P. Zoller. Cold Bosonic Atoms in Optical Lattices [J]. Phys. Rev. Lett.,1998,81:3108.
[84]P. Anders, E. Gull, L. Pollet, M. Troyer, P. Werner. Dynamical Mean Field Solution of the Bose-Hubbard Model [J]. Phys. Rev. Lett.,2010,105:096402.
[85]C. Trefzger, K. Sengupta. Nonequilibrium Dynamics of the Bose-Hubbard Mod-el:A Projection-Operator Approach [J]. Phys. Rev. Lett.,2011,106:095702.
[86]B. L. Chen, S. P. Kou, Y. Zhang, S. Chen. Quantum phases of the Bose-Hubbard model in optical superlattices [J]. Phys. Rev. A,2010,81:053608.
[87]K. Sakmann, A. I. Streltsov,0. E. Alon, L. S. Cederbaum. Quantum dynamics of attractive versus repulsive bosonic Josephson junctions:Bose-Hubbard and full-Hamiltonian results [J]. Phys. Rev. A,2010,82:013620.
[88]M. Collura, H. Aufderheide, G. Roux, D. Karevski. Entangling many-body bound states with propagative modes in Bose-Hubbard systems [J]. Phys. Rev. A,2012,86:013615.
[89]M. Pino, J. Prior. A. M. Somoza, D. Jaksch, S. R. Clark. Reentrance and entanglement in the one-dimensional Bose-Hubbard model [J]. Phys. Rev. A, 2012,86:023631.
[90]K. Ziegler. Dynamics of two-site Fermi-Hubbard and Bose-Hubbard systems [J]. Phys. Rev. A,2010,81:034701.
[91]S. Longhi. Optical realization of the two-site Bose-Hubbard model in waveguide lattices [J]. J. Phys. B,2011,44:051001.
[92]M. Mele-Messeguer, B. Julia-Diaz, A. Polls. Improved Variational Approach to the Two-Site Bose-Hubbard Model [J]. J. Low. Temp. Phys.,2011,165:180.
[93]G. Mazzarella, L. Salasnich, A. Parola, F. Toigo. Coherence and entangle-ment in the ground state of a bosonic Josephson junction:From macroscopic Schrodinger cat states to separable Fock states [J]. Phys. Rev. A,2011,83: 053607.
[94]L. Dell'Anna. Analytical approach to the two-site Bose-Hubbard model:From Fock states to Schrodinger cat states and entanglement entropy [J]. Phys. Rev. A,2012,85:053608.
[95]M. Greiner, O. Mandel, T. Esslinger, T. W. Hansch, I. Bloch. Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms [J]. Nature.2002,415:39.
[96]P. Buonsante, A. Vezzani. Ground-State Fidelity and Bipartite Entanglement in the Bose-Hubbard Model [J]. Phys. Rev. Lett.,2007,98:110601.
[97]X. Deng, L. Santos. Entanglement spectrum of one-dimensional extended Bose-Hubbard models [J]. Phys. Rev. B,2011,84:085138.
[98]K. K. Xg, Y. C. Chen, Y. C. Tzeng. Quarter-filled supersolid and solid phases in the extended Bose-Hubbard model [J]. J. Phys.:Condens. Matter,2010.22: 185601.
[99]M. S. Underwood, D. L. Feder. Bose-Hubbard model for universal quantum-walk-based computation [J]. Phys. Rev. A,2012,85:052314.
[100]M. Oktel, M. Nit;a, B. Tanatar. Mean-field theory for Bose-Hubbard m.odel under a magnetic field [J]. Phys. Rev. B,2007,73:045133.
[101]S. Ejima, H. Fehske, F. Gebhard. Dynamic properties of the one-dimensional Bose-Hubbard model [J]. Europhys. Lett.,2011,93:30002.
[102]D. Rossini, R. Fazio. Phase diagram of the extended Bose-Hubbard model [J]. New J. Phys.,2012,14:065012.
[103]J. M. Zhang. R. X. Dong. Exact diagonalization:the Bose-Hubbard model as an example [J]. Eur. J. Phys.,2010,31:591.
[104]L. Wang, Y. Hao, S. Chen. Quantum dynamics of repulsively bound atom pairs in the Bose-Hubbard model [J]. Eur. Phys. J. D,2008,48:229.
[105]N. Teichmann, D. Hinrichs, M. Holthaus. Process-chain approach to the Bose-Hubbard model:Ground-state properties and phase diagram [J]. Phys. Rev. B, 2009,79:224515.
[106]G. Mazzarella, M. Moratti, L. Salasnich, F. Toigo. Nonlinear quantum model for atomic Josephson junctions with one and two bosonic species [J]. J. Phys. B,2010,43:065303.
[107]H. P. Breuer, E. M. Laine, J. Piilo. Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems [J]. Phys. Rev. Lett.,2009, 103:210401.
[108]E. M. Laine, J. Piilo. H. P. Breuer. Measure for the non-Markovianity of quantum processes [J]. Phys. Rev. A,2010,81:062115.
[109]B. Julia-Diaz, D. Dagnino, M. Lewenstein, J. Martorell. A. Polls. Macroscopic self-trapping in Bose-Einstein condensates:Analysis of a dynamical quantum phase transition [J]. Phys. Rev. A,2010,81:023615.
[110]T. Yu. Entanglement decay versus energy change:A m.odel [J]. Phys. Lett. A, 2007,361:287.
[111]C. Gollub, U. Troppmann, R. de Vivie-Riedle. The role of anharmonicity and coupling in quantum computing based on vibrational qubits [J]. New J. Phys., 2006,8:48.
[112]C. M. Tesch, R. de Vivie-Riedle R Vibrational molecular quantum comput-ing:Basis set independence and theoretical realization of the Deutsch-Jozsa algorithm [J]. J. Chem. Phys.,2004,121:12158.
[113]B. M. R. Korff, U. Troppmann, K. L. Kompa. R. de Vivie-Riedle. Manganese pentacarbonyl bromide as candidate for a molecular qubit system operated in the infrared regime [J]. J. Chem. Phys.,2005,123:244509.
[114]U. Troppmann, C. Gollub, R. de Vivie-Riedle. The role of phases and their interplay in molecular vibrational quantum computing with multiple qubits [J]. New J. Phys.,2006,8:100.
[115]W. Zhu, J. Botina, H Rabitz. Rapidly convergent iteration methods for quan-tum optimal control of population [J]. J. Chem. Phys.,1998,108:1953.
[116]Y. Ohtsuki, W. Zhu, H. Rabitz. Monotonically convergent algorithm for quan-tum optimal control with dissipation [J]. J. Chem. Phys.,1999,110:9825.
[117]J. P. Palao, R. Kosloff. Optimal control theory for unitary transformations [J]. Phys. Rev. A,2003,68:062308.
[118]K. Mishima, K. Yamsshita. Decoherence of intramolecular vibrational entan-glement in polyatomic molecules [J]. Int. J. Quantum Chem.,2009,109:1827.
[119]M. C. Tichy. F. Mintert, A. Buchleitner. Essential entanglement for atomic and molecular physics [J]. J. Phys. B,2011,44:192001.
[120]T. Yu, J. H. Eberly. Sudden Death of Entanglement [J]. Science,2009,323: 598.
[121]A. C. Scott, J. C. Eilbeck. The quantized discrete self-trapping equation [J]. Phys. Lett. A,1986,119:60.
[122]S. Bose:V. Vedral. Mixedness and teleportation [J]. Phys. Rev. A,2000,61: 040101.
[123]F. Iachello, R. D. Levine. Algebraic Theory of Molecules [M]. New Youk: Oxford University Press,1995.
[124]Z. Xu, Y. Gao, Calculation of vibrational spectroscopy for tri-atomic molecules using interaction model [J]. Acta Phys.-Chim. Sin.,1996,12:555.
[125]J. Gambetta, A. Blais, D. I. Schuster, A. Wallraff, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, R. J. Schoelkopf. Qubit-photon interactions in a cavity: Measurement-induced dephasing and number splitting [J]. Phys. Rev. A,2006, 74:042318.
[126]M. Yonac, T. Yu, J. H. Eberly. Pairunse concurrence dynamics:a four-qubit model [J]. J. Phys. B,2007,40:s45.
[127]K. Kraus. States, Effects, and Operations [M]. Berlin:Springer,1983.
[128]M. A. Nielsen and I. L. Chuang Quantum Compuation and Quantum Infor-mation [M]. Cambridge:Cambridge University Press,2000.
[129]R. Alicki, K. Lendi. Quantum Dynamical Semigroups and Applications [M]. Berlin:Springer,2007.
[130]T. F. Jordan, A. Shaji, E. C. G. Sudarshan. Dynamics of initially entangled open quantum systems [J]. Phys. Rev. A,2004,70:052110.
[131]H. A. Carteret, D. R. Terno, K. Zyczkowski. Dynamics beyond completely positive maps:Some properties and applications [J]. Phys. Rev. A,2008,77: 042113.
[132]A. Shabani, D. A. Lidar. Vanishing Quantum Discord is Necessary and Suf-ficient for Completely Positive Maps [J]. Phys. Rev. Lett.,2009,102:100402.
[133]C.-F. Li, J.-S. Tang, Y.-L. Li, G.-C. Guo. Experimentally witnessing the initial correlation between an open quantum system and its environment [J]. Phys. Rev. A.2011,83:064102.
[134]A. Smirne, D. Brivio, S. Cialdi, B. Vacchini, M. G. A. Paris. Experimen-tal investigation of initial system-environment correlations via trace-distance evolution [J]. Phys. Rev. A,2011,84:032112.
[135]G. V. Varada, G. S. Agarwal. Two-photon resonance induced by the dipole-dipole interaction [J]. Phys. Rev. A,1992,45:6721.
[136]C. Hettich, C. Schmitt, J. Zitzmann, S. Kuhn, I. Gerhardt, V. Sandoghdar. Nanometer Resolution and Coherent Optical Dipole Coupling of Two Individual Molecules [J]. Science,2002,298:385.
[137]J. H. Reina, R. G. Beausoleil, T. P. Spiller, W. J. Munro. Radiative Correc-tions and Quantum Gates in Molecular Systems [J]. Phys. Rev. Lett.,2004, 93:250501.
[138]D. Z. Rossatto, T. Werlang, L. K. Castelano, C. J. Villas-Boas, F. F. Fanchini. Purity as a witness for initial system-environment correlations in open-system dynamics [J]. Phys. Rev. A,2011,84:042113.