超冷原子规则和混沌输运的相干控制
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摘要
输运现象是物理学中许多问题的核心。近年来,利用外场相干控制有相互作用的超冷原子的输运吸引了人们极大的兴趣。本文以Bose-Hubbard模型和GP方程为基础分别研究了两个相互作用玻色原子和玻色爱因斯坦凝聚体在周期驱动场下的隧穿动力学。全文分为五章,作者自己的研究工作主要集中在第二、三、四章。文章安排如下：
第一章为绪论,简要介绍超冷原子物理的发展和量子阱的实验制备,以及少原子在紧束缚模型中的动力学现象和玻色爱因斯坦凝聚体的输运现象。
第二章,我们研究了囚禁在三阱势中的两个排斥玻色子在高频驱动场下的量子隧穿。利用多时间尺度渐近分析,我们证实了在远离共振强的相互作用区域中对态的主要隧穿动力学是二级隧穿,并且在这个区域中对态之间或者非对态之间会出现选择性的隧穿相干破坏。两类态的Floquet准能带被解析给出,准能带中到二级修正项的精细结构也被展示出来。基于精确的模型,解析结果被数值结果证实。这些结果在实验中对控制关联隧穿特别相关。长时间尺度的二级隧穿能方便地用来绝热操控对态粒子的关联隧穿,并且可以作为进一步理解在驱动晶格系统中粒子输运行为的基础。三阱系统的结果也能推广到三能级系统和三个量子点系统,展现出更丰富的物理现象。
第三章,我们研究了囚禁在含有一个杂质光学晶格中两个玻色子在时间周期驱动下的相干控制。在高频近似下我们利用幺正变换解析地推导出了不含时的有效哈密顿量。在动力学局域化条件下我们研究了杂质和原子间相互作用强度对两个原子动力学的影响。当杂质势强度和交流驱动频率的比值是整数时两个原子会在含有杂质的格点和两个相邻格点间发生隧穿。原子间是弱的相互作用时,两个原子能在三个格点中分开运动。但是原子间是强的相互作用时,两个原子不会分开而是以束缚对的形式隧穿。当原子间的相互作用强度等于杂质势的强度时两个原子在全光学晶格中发生CDT,两者之比为其它整数时,由于能从驱动场吸引能量两个原子趋向于分开运动。
第四章,使用有效粒子近似方法,我们研究了双周期驱动下囚禁在准一维对称光学超晶格中利用时间棘齿效应混沌输运由相互吸引的玻色爱因斯坦凝聚体所组成的物质波孤子。在安德森情景中,众所周知混沌能够代替无序。对于某些特殊系统更高程度的无序能诱使安德森局域化。在高或者低混沌区域中物质波孤子会以高或者低概率转变成混沌。我们证实在低频率和适度频率区域,通过变化驱动位相来打破系统的时间反演对称性能增大高混沌区域的大小。空间指数局域化的参数区域将相应地增大相同的大小,那么包括棘齿效应区域和它的反效应区域的低混沌区域和去局域化区域相应地减小。局域化相对于驱动频率的正相关也被揭示。这些结果表明高混沌能够代替高度无序,从而帮助安德森局域化。从这些结论出发,我们提出通过调节驱动频率和振幅增强或者抑制,甚至反转时间棘齿效应,来控制物质波孤子的定向运动。
第五章,我们对本文工作进行了总结,并对时空周期势中超冷原子的输运这个研究领域的前景作了简单的展望。
Transport phenomena are the heart of many problems in physics. In recent years, the coherent control of interacting ultracold atomic transport by employing external field has attracted great interest. We investigate the tunneling dynamics of two interacting bosons and Bose-Einstein condensate in this thesis via utilizing a periodic driving field, based on the Bose-Hubbard model and GP equation, respectively. The thesis is divided into five chapters. Our own main works are concentrated on the chapters two, three and four. This thesis is organized as follows.
In the first chapter, we give a brief introduction about the development of ultracold atom physics and the experimental realization of quantum well, and the dynamics of few-atom held in tight-binding model and transport phenomena of Bose-Einstein condensate.
In chapter two, we investigate quantum tunneling of two repulsive bosons in a triple-well potential subject to a high-frequency driving field. By means of the multiple-time-scale asymptotic analysis, we evidence a far-off-resonant strongly-interacting regime in which the dominant tunneling of paired states is a second order process, and the selected coherent destruction of tunneling occurs either be-tween doublons, or between unpaired states. Two Floquet quasienergy bands of the both kinds of states are given analytically, where a fine structure up to the second order corrections is displayed. The analytical results are confirmed numerically based on the exact model, and may be particularly relevant to controlling corre-lated tunneling in experiments. The second order results of long time scale could be conveniently applied to adiabatic manipulation of the paired particle correlated tunneling, and may serve as a useful stepping stone to understand the transport behavior of particles in a driven lattice system. The results from the triple-well system can also be extended to the three-level system and triple-quantum-dot system, exhibiting richer new physics.
In chapter three, we investigate the coherent control of two bosons held in a one-dimensional optical lattices with an impurity via time-periodic driving field. In the high-frequency driving regime, we deduce analytically the time-independent effective Hamiltonian by using a unitary transformation. We study the effects of the impurity and the interaction strength between the atoms on the dynamics of the two atoms in the dynamic localization condition. The tunneling of two atoms can take place between the impurity and its two nearest-neighbor sites when the ratio of the impurity potential strength and the ac driving frequency is an integer. For weakly interacting strength of atoms, the atoms can move independently around the three sites, but for more strongly interacting strength, the atoms can form a stable bound pair, and they cannot move independently. Two atoms will occur CDT in the whole optical lattice when the interaction strength between the atoms is equal to the impurity strength. When the ratio of the interaction strength and the impurity strength becomes other integers, the atoms tend to separate due to they can absorb energy from the driving field.
In chapter four, under the effective particle approximation, we study temporal ratchet effect for chaotically transporting a matter-wave soliton consisting of an attractive Bose-Einstein condensate held in a quasi-one-dimensional symmetric optical supperlattice with biperiodic driving. It has been known that chaos can substitute for disorder in Anderson's scenario and only a higher level of disorder can induce Anderson localization for some special systems, and a matter-wave soliton could transit to chaos with high or low probability in the high-or low-chaoticity region. We demonstrate that varying the driving phase to break time reversal symmetry of the system can enlarge a size of the high-chaoticity region for the low-and moderate-frequency regions. Consequently, the parameter region of exponential spatial localization is enlarged the same size and the delocalization region which includes the subregions of ratchet effect and its reversal related to the low chaoticity is correspondingly shorten. The positive dependence of the localization on the driving frequency has also been revealed. The results mean that the high-chaoticity could replace the higher disorder and assists Anderson localization. From the results we suggest a method for controlling directed motion of the matter-wave soliton by adjusting the driving frequency and amplitudes to strengthen or suppress even reverse the temporal ratchet effect.
In chapter five, we give a conclusion of the work and an outlook about the transport of ultracold atom in the spatiotemporal potential.
第一章为绪论,简要介绍超冷原子物理的发展和量子阱的实验制备,以及少原子在紧束缚模型中的动力学现象和玻色爱因斯坦凝聚体的输运现象。
第二章,我们研究了囚禁在三阱势中的两个排斥玻色子在高频驱动场下的量子隧穿。利用多时间尺度渐近分析,我们证实了在远离共振强的相互作用区域中对态的主要隧穿动力学是二级隧穿,并且在这个区域中对态之间或者非对态之间会出现选择性的隧穿相干破坏。两类态的Floquet准能带被解析给出,准能带中到二级修正项的精细结构也被展示出来。基于精确的模型,解析结果被数值结果证实。这些结果在实验中对控制关联隧穿特别相关。长时间尺度的二级隧穿能方便地用来绝热操控对态粒子的关联隧穿,并且可以作为进一步理解在驱动晶格系统中粒子输运行为的基础。三阱系统的结果也能推广到三能级系统和三个量子点系统,展现出更丰富的物理现象。
第三章,我们研究了囚禁在含有一个杂质光学晶格中两个玻色子在时间周期驱动下的相干控制。在高频近似下我们利用幺正变换解析地推导出了不含时的有效哈密顿量。在动力学局域化条件下我们研究了杂质和原子间相互作用强度对两个原子动力学的影响。当杂质势强度和交流驱动频率的比值是整数时两个原子会在含有杂质的格点和两个相邻格点间发生隧穿。原子间是弱的相互作用时,两个原子能在三个格点中分开运动。但是原子间是强的相互作用时,两个原子不会分开而是以束缚对的形式隧穿。当原子间的相互作用强度等于杂质势的强度时两个原子在全光学晶格中发生CDT,两者之比为其它整数时,由于能从驱动场吸引能量两个原子趋向于分开运动。
第四章,使用有效粒子近似方法,我们研究了双周期驱动下囚禁在准一维对称光学超晶格中利用时间棘齿效应混沌输运由相互吸引的玻色爱因斯坦凝聚体所组成的物质波孤子。在安德森情景中,众所周知混沌能够代替无序。对于某些特殊系统更高程度的无序能诱使安德森局域化。在高或者低混沌区域中物质波孤子会以高或者低概率转变成混沌。我们证实在低频率和适度频率区域,通过变化驱动位相来打破系统的时间反演对称性能增大高混沌区域的大小。空间指数局域化的参数区域将相应地增大相同的大小,那么包括棘齿效应区域和它的反效应区域的低混沌区域和去局域化区域相应地减小。局域化相对于驱动频率的正相关也被揭示。这些结果表明高混沌能够代替高度无序,从而帮助安德森局域化。从这些结论出发,我们提出通过调节驱动频率和振幅增强或者抑制,甚至反转时间棘齿效应,来控制物质波孤子的定向运动。
第五章,我们对本文工作进行了总结,并对时空周期势中超冷原子的输运这个研究领域的前景作了简单的展望。
Transport phenomena are the heart of many problems in physics. In recent years, the coherent control of interacting ultracold atomic transport by employing external field has attracted great interest. We investigate the tunneling dynamics of two interacting bosons and Bose-Einstein condensate in this thesis via utilizing a periodic driving field, based on the Bose-Hubbard model and GP equation, respectively. The thesis is divided into five chapters. Our own main works are concentrated on the chapters two, three and four. This thesis is organized as follows.
In the first chapter, we give a brief introduction about the development of ultracold atom physics and the experimental realization of quantum well, and the dynamics of few-atom held in tight-binding model and transport phenomena of Bose-Einstein condensate.
In chapter two, we investigate quantum tunneling of two repulsive bosons in a triple-well potential subject to a high-frequency driving field. By means of the multiple-time-scale asymptotic analysis, we evidence a far-off-resonant strongly-interacting regime in which the dominant tunneling of paired states is a second order process, and the selected coherent destruction of tunneling occurs either be-tween doublons, or between unpaired states. Two Floquet quasienergy bands of the both kinds of states are given analytically, where a fine structure up to the second order corrections is displayed. The analytical results are confirmed numerically based on the exact model, and may be particularly relevant to controlling corre-lated tunneling in experiments. The second order results of long time scale could be conveniently applied to adiabatic manipulation of the paired particle correlated tunneling, and may serve as a useful stepping stone to understand the transport behavior of particles in a driven lattice system. The results from the triple-well system can also be extended to the three-level system and triple-quantum-dot system, exhibiting richer new physics.
In chapter three, we investigate the coherent control of two bosons held in a one-dimensional optical lattices with an impurity via time-periodic driving field. In the high-frequency driving regime, we deduce analytically the time-independent effective Hamiltonian by using a unitary transformation. We study the effects of the impurity and the interaction strength between the atoms on the dynamics of the two atoms in the dynamic localization condition. The tunneling of two atoms can take place between the impurity and its two nearest-neighbor sites when the ratio of the impurity potential strength and the ac driving frequency is an integer. For weakly interacting strength of atoms, the atoms can move independently around the three sites, but for more strongly interacting strength, the atoms can form a stable bound pair, and they cannot move independently. Two atoms will occur CDT in the whole optical lattice when the interaction strength between the atoms is equal to the impurity strength. When the ratio of the interaction strength and the impurity strength becomes other integers, the atoms tend to separate due to they can absorb energy from the driving field.
In chapter four, under the effective particle approximation, we study temporal ratchet effect for chaotically transporting a matter-wave soliton consisting of an attractive Bose-Einstein condensate held in a quasi-one-dimensional symmetric optical supperlattice with biperiodic driving. It has been known that chaos can substitute for disorder in Anderson's scenario and only a higher level of disorder can induce Anderson localization for some special systems, and a matter-wave soliton could transit to chaos with high or low probability in the high-or low-chaoticity region. We demonstrate that varying the driving phase to break time reversal symmetry of the system can enlarge a size of the high-chaoticity region for the low-and moderate-frequency regions. Consequently, the parameter region of exponential spatial localization is enlarged the same size and the delocalization region which includes the subregions of ratchet effect and its reversal related to the low chaoticity is correspondingly shorten. The positive dependence of the localization on the driving frequency has also been revealed. The results mean that the high-chaoticity could replace the higher disorder and assists Anderson localization. From the results we suggest a method for controlling directed motion of the matter-wave soliton by adjusting the driving frequency and amplitudes to strengthen or suppress even reverse the temporal ratchet effect.
In chapter five, we give a conclusion of the work and an outlook about the transport of ultracold atom in the spatiotemporal potential.
引文
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