光晶格中超冷原子系综的动力学性质
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摘要
光晶格中超冷原子系综的物理特性是冷原子物理这一新领域中的重要研究课题。这一研究之所以成为当前一个热点的主要原因是光晶格中的超冷原子系综为模拟传统凝聚体物理和固体物理中的复杂物理问题提供了一个理想模型。由于不存在任何杂质和缺陷的特点和高可控性使得光晶格中的冷原子系综成为一个良好工具,我们甚至可以用它去研究一些凝聚态物理中从来没有的新奇的量子现象。
当前有关光晶格中的超冷原子的研究涉及到许多方面。其中有两个重要方面是我们感兴趣的。一方面,光晶格为研究超冷原子的磁学性质和自旋相关动力学提供了一种有效的研究工具,特别是光晶格中的自旋波激发、控制和探测的研究将为BEC在量子计算与量子信息处理等方面的应用提供重要的指导。然而目前这一方面的研究仅仅处于开始阶段。有许多科学问题有待解决。例如,与凝聚态物理中磁性晶格的自旋链模型相比较,光晶格中由于光诱导的长程相互作用的存在,其自旋动力学特性展现出更加丰富多彩的物理内涵。
另一方面,近年来随着实验上冷却和囚禁具有较大磁偶极距的超冷原子气体的实现,磁偶极-偶极相互作用对超冷原子气体动力学性质的影响正逐渐成为理论和实验上的一个热点研究课题。与此同时,布洛赫振荡这个固体物理中的基本现象在超冷原子体系中被观测到以后,由于其比较窄的动量谱分布,被广泛应用于超高精密测量,如何提高其测量精度也是目前人们正面对的课题。
本论文就针对以上两个方面的问题展开深入研究。论文的前两章属于对背景知识的回顾,论文的第一章简述了激光冷却原子技术和玻色-爱因斯坦凝聚的实现。第二章介绍了光晶格的实现、性质以及光晶格中的旋量BEC和偶极气体的特性,为我们所要做的研究工作做好铺垫。
第三章应用平均场理论处理方法,对旋量BEC原子自旋链中的内禀局域自旋波模进行了研究。数值分析了内禀局域模的性质以及其和长程耦合相互作用的关系。展现了长程相互作用在确定光晶格中自旋动力学方面的不可忽视的角色。同时也表明由于光晶格中原子之间长程偶极相互作用的存在,光晶格超冷原子系综为研究格点系统中更为丰富自旋耦合动力学特性提供了一个理想的工具,也为超冷原子向量子信息科学与凝聚态物理交叉领域的发展提供了广阔的前景。
第四章中我们研究了磁偶极-偶极相互作用对光晶格中超冷原子气体的布洛赫振荡的影响。我们首先推导出准一维光晶格中偶极气体的Gross-Pitaevskii方程,详细分析了磁偶极-偶极相互作用的傅里叶谱,得到了一个魔幻极化方向。这个方向上磁偶极-偶极相互作用对系统没有贡献。我们将这个魔幻极化方向应用到超冷原子的布洛赫振荡中,研究了这个极化方向对提高原子系综的相干性以及布洛赫振荡在超高精密测量中的精度的重要作用。
最后在第五章中,我们对我们的研究作了概括性的总结,并在此基础上,对未来的发展进行了展望。
The physical property of the ultra-cold atomic ensemble in optical lattice is one of the important topics in cold atom physics. Recently the study of ultra-cold atoms in periodic potentials becomes a hot physical topic, because it can mimic many complicated problems encountered in traditional condensed matter and solid state physics. With no impurity and defect and high controllability, the system of ultra-cold atomic ensemble in optical lattice provides us a powerful tool to investigate the quantum phenomenas which do not exist in traditional condensed matter.
The recent studies about ultra-cold atoms in optical lattice involve many aspects and we are interesting in two of them. On the one hand, the optical lattice can provide us a powerful tool in the field of spin dynamics and atomic magnetic properties. Among them, the dynamic processes such as spin wave excitations, controlling and detection, will provide useful information in quantum calculation and quantum information when Bose-Einstein condensates (BEC) are used in these areas. However, the study on this field is just emerging. So there exist many open problems for us to solve. For example, due to the existence of long range interaction induced by optical field, the spin dynamics will exhibit many interesting novel physical behaviors.
On the other hand, after cooling and trapping ultra-cold atom gases with larger magnetic dipoles have been realized in laboratory, the effect of dipole-dipole interaction on the dynamics of ultra-cold atom gases is emerging as a hot topic of intensive theoretical and experimental investigation. Meanwhile, Bloch oscillations as one of the fundamental solid state phenomena has been investigated in ultra-cold atomic ensembles, in which Bloch oscillations can be measured with a higher precision thanks to the smaller width of the momentum distribution. It has been taken as a tool of ultrahigh precision measurement. The problem that physicists are facing is how to improve the accuracy.
This thesis tries to extensively and thoroughly deal with above problems. Some fundamental background knowledge is reviewed in first two chapters. In the first chapter, we simply reviewed laser coolling techniques and realization of BEC. In the second chapter, we first reviewed the realization and properties of optical lattice and BECs confined in it, then we focus on spinor BECs and dipolar gases whose dynamics will be investigated in residual chapters.
In the third chapter, by using the mean field approach method, the intrinsic localized spin wave modes in spinor BECs atomic spin chain with strong light-induced dipole-dipole interaction are studied, which show that the long range interaction in this system plays an important role. The long range interaction in optical lattice provides us a powerful tool in the field of studying the effect of nonlinear interaction on spin dynamics in the discrete lattice systems. It also presents a broad prospect for the development of the crossover of quantum information and condensed matter.
In the fourth chapter, we have studied the effect of magnetic dipole-dipole interaction on the envelope dynamics of ultra-cold atom gases in an optical lattice. For a quasi-one-dimensional dipolar gas, we have derived the Gross-Pitaeskii equation with a magnetic dipole-dipole interaction. After studying the Fourier spectrum, we find a magical polarization direction along which the repulsive interaction and attractive interaction cancel out each other. We study the dependence of Bloch oscillations on this magical polarization direction, and find it improves the Bloch oscillations to some extended.
In the final chapter, we conclude the thesis and propose possible development.
当前有关光晶格中的超冷原子的研究涉及到许多方面。其中有两个重要方面是我们感兴趣的。一方面,光晶格为研究超冷原子的磁学性质和自旋相关动力学提供了一种有效的研究工具,特别是光晶格中的自旋波激发、控制和探测的研究将为BEC在量子计算与量子信息处理等方面的应用提供重要的指导。然而目前这一方面的研究仅仅处于开始阶段。有许多科学问题有待解决。例如,与凝聚态物理中磁性晶格的自旋链模型相比较,光晶格中由于光诱导的长程相互作用的存在,其自旋动力学特性展现出更加丰富多彩的物理内涵。
另一方面,近年来随着实验上冷却和囚禁具有较大磁偶极距的超冷原子气体的实现,磁偶极-偶极相互作用对超冷原子气体动力学性质的影响正逐渐成为理论和实验上的一个热点研究课题。与此同时,布洛赫振荡这个固体物理中的基本现象在超冷原子体系中被观测到以后,由于其比较窄的动量谱分布,被广泛应用于超高精密测量,如何提高其测量精度也是目前人们正面对的课题。
本论文就针对以上两个方面的问题展开深入研究。论文的前两章属于对背景知识的回顾,论文的第一章简述了激光冷却原子技术和玻色-爱因斯坦凝聚的实现。第二章介绍了光晶格的实现、性质以及光晶格中的旋量BEC和偶极气体的特性,为我们所要做的研究工作做好铺垫。
第三章应用平均场理论处理方法,对旋量BEC原子自旋链中的内禀局域自旋波模进行了研究。数值分析了内禀局域模的性质以及其和长程耦合相互作用的关系。展现了长程相互作用在确定光晶格中自旋动力学方面的不可忽视的角色。同时也表明由于光晶格中原子之间长程偶极相互作用的存在,光晶格超冷原子系综为研究格点系统中更为丰富自旋耦合动力学特性提供了一个理想的工具,也为超冷原子向量子信息科学与凝聚态物理交叉领域的发展提供了广阔的前景。
第四章中我们研究了磁偶极-偶极相互作用对光晶格中超冷原子气体的布洛赫振荡的影响。我们首先推导出准一维光晶格中偶极气体的Gross-Pitaevskii方程,详细分析了磁偶极-偶极相互作用的傅里叶谱,得到了一个魔幻极化方向。这个方向上磁偶极-偶极相互作用对系统没有贡献。我们将这个魔幻极化方向应用到超冷原子的布洛赫振荡中,研究了这个极化方向对提高原子系综的相干性以及布洛赫振荡在超高精密测量中的精度的重要作用。
最后在第五章中,我们对我们的研究作了概括性的总结,并在此基础上,对未来的发展进行了展望。
The physical property of the ultra-cold atomic ensemble in optical lattice is one of the important topics in cold atom physics. Recently the study of ultra-cold atoms in periodic potentials becomes a hot physical topic, because it can mimic many complicated problems encountered in traditional condensed matter and solid state physics. With no impurity and defect and high controllability, the system of ultra-cold atomic ensemble in optical lattice provides us a powerful tool to investigate the quantum phenomenas which do not exist in traditional condensed matter.
The recent studies about ultra-cold atoms in optical lattice involve many aspects and we are interesting in two of them. On the one hand, the optical lattice can provide us a powerful tool in the field of spin dynamics and atomic magnetic properties. Among them, the dynamic processes such as spin wave excitations, controlling and detection, will provide useful information in quantum calculation and quantum information when Bose-Einstein condensates (BEC) are used in these areas. However, the study on this field is just emerging. So there exist many open problems for us to solve. For example, due to the existence of long range interaction induced by optical field, the spin dynamics will exhibit many interesting novel physical behaviors.
On the other hand, after cooling and trapping ultra-cold atom gases with larger magnetic dipoles have been realized in laboratory, the effect of dipole-dipole interaction on the dynamics of ultra-cold atom gases is emerging as a hot topic of intensive theoretical and experimental investigation. Meanwhile, Bloch oscillations as one of the fundamental solid state phenomena has been investigated in ultra-cold atomic ensembles, in which Bloch oscillations can be measured with a higher precision thanks to the smaller width of the momentum distribution. It has been taken as a tool of ultrahigh precision measurement. The problem that physicists are facing is how to improve the accuracy.
This thesis tries to extensively and thoroughly deal with above problems. Some fundamental background knowledge is reviewed in first two chapters. In the first chapter, we simply reviewed laser coolling techniques and realization of BEC. In the second chapter, we first reviewed the realization and properties of optical lattice and BECs confined in it, then we focus on spinor BECs and dipolar gases whose dynamics will be investigated in residual chapters.
In the third chapter, by using the mean field approach method, the intrinsic localized spin wave modes in spinor BECs atomic spin chain with strong light-induced dipole-dipole interaction are studied, which show that the long range interaction in this system plays an important role. The long range interaction in optical lattice provides us a powerful tool in the field of studying the effect of nonlinear interaction on spin dynamics in the discrete lattice systems. It also presents a broad prospect for the development of the crossover of quantum information and condensed matter.
In the fourth chapter, we have studied the effect of magnetic dipole-dipole interaction on the envelope dynamics of ultra-cold atom gases in an optical lattice. For a quasi-one-dimensional dipolar gas, we have derived the Gross-Pitaeskii equation with a magnetic dipole-dipole interaction. After studying the Fourier spectrum, we find a magical polarization direction along which the repulsive interaction and attractive interaction cancel out each other. We study the dependence of Bloch oscillations on this magical polarization direction, and find it improves the Bloch oscillations to some extended.
In the final chapter, we conclude the thesis and propose possible development.
引文
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