超冷原子气体中的拓扑态：非常规晶格与相互作用效应
发布时间：2018-09-17 06:56
【摘要】：在这篇论文中,我们描述了对于超冷原子气体体系中拓扑态的三个研究工作.在前两个工作中,我们分别提出了两个在超冷原子体系中合成二维拓扑晶格的实验方案.在第三个工作中,我们描述了用极化偶极费米气体实现一维拓扑超导体(Kitaev链)的方案,并着重研究了其中的相互作用效应.在第一个工作中,我们提出了一种基于相位刻印技术,用磁场脉冲序列来合成拓扑非平庸的磁晶格的实验方案.这个方案生成的等效哈密顿量,在绝热极限下可以映射到Haldane的拓扑陈绝缘体模型.通过调节磁场参数,我们可以驱动哈密顿量的最低能带发生一个由拓扑陈绝缘体到拓扑平庸的绝缘体之间的拓扑相变,在相变点附近可以实现拓扑平带.在第二个工作中,我们提出了用调幅的Raman激光以及射频磁场来生成具有拓扑非平庸能带结构的光通量晶格的实验方案.这个方案合成的不含时的等效哈密顿量的最低能带的拓扑性质依赖于Raman激光以及射频磁场的强度.我们考察了不同的Raman激光以及射频磁场强度下,等效哈密顿量的能带以及相应的陈数,并由此得到了系统在单填充下的基态相图.在相图中包含三个不同的相:拓扑陈绝缘体相,正常绝缘体相,以及半金属相.这个方案同样可以实现Haldane模型,拓扑相变,以及拓扑平带.在第三个工作中,我们描述了用极化偶极费米气体实现一维相互作用拓扑超导体的方案.我们用严格对角化的数值方法计算了相互作用下系统的能谱,并由此得到了以相互作用强度以及化学势为参数的基态相图.相图中包含五个相:填充数为一的绝缘体相,填充数为零的真空相,填充数为1/2的Mott绝缘体相,拓扑超导体相,以及Luttinger液体相.我们用基态能隙,保真度极化率,基态粒子数宇称,以及基态的压缩率等物理量描述了基态不同相的性质.我们计算了相互作用下的Majorana零模波函数,描述了基态的纠缠性质(纠缠谱,纠缠熵,中心荷),并且通过有限尺寸标度的方法证实了Luttinger液体态元激发无能隙的特性.
[Abstract]:In this paper, we describe three studies of topological states in supercooled atomic gas systems. In the first two works, we have proposed two experimental schemes for the synthesis of two-dimensional topological lattices in ultra-cold atomic systems. In the third work, we describe the scheme of using polarized dipole Fermi gas to realize one-dimensional topological superconductors (Kitaev chains), and focus on the study of the interaction effect. In the first work, we propose an experimental scheme for the synthesis of topological nonmediocre magnetic lattices using magnetic pulse sequences based on phase lithography. The equivalent Hamiltonian generated by this scheme can be mapped to Haldane's topological old insulator model under adiabatic limit. By adjusting the magnetic field parameters, we can drive the lowest energy band of Hamiltonian to take place a topological phase transition between the topological Chen insulator and the topological mediocre insulator. The topological flat band can be realized near the phase transition point. In the second work, we propose an experimental scheme for the generation of luminous flux lattices with topologically nonmediocre band structures using amplitude modulated Raman lasers and RF magnetic fields. The topological properties of the minimum energy band of the time-free equivalent Hamiltonian synthesized by this scheme depend on the intensity of Raman laser and RF magnetic field. We investigate the energy bands of equivalent Hamiltonian and the corresponding aging numbers at different Raman laser and RF magnetic field intensities, and obtain the ground state phase diagram of the system under single filling. There are three different phases in the phase diagram: topological old insulator phase, normal insulator phase, and semi-metallic phase. This scheme can also achieve Haldane model, topological phase transition, and topological flat band. In the third work, we describe the scheme of one-dimensional interacting topological superconductors using polarized dipole Fermi gas. The energy spectrum of the system under interaction is calculated by strictly diagonalized numerical method, and the ground state diagram with the interaction intensity and chemical potential as parameters is obtained. There are five phases in the phase diagram: the insulator phase with one filling number, the vacuum phase with zero filling number, the Mott insulator phase with 1 / 2 filling number, the topological superconductor phase and the Luttinger liquid phase. The properties of different phases in the ground state are described by means of the ground state energy gap, the fidelity polarizability, the parity of the ground state population and the squeezing ratio of the ground state. We calculate the Majorana zero-mode wave function under the interaction, describe the entanglement properties of the ground state (entanglement spectrum, entanglement entropy, central charge), and prove the characteristics of the Luttinger liquid state element excited without energy gap by the finite scale method.
【学位授予单位】：清华大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O469
[Abstract]:In this paper, we describe three studies of topological states in supercooled atomic gas systems. In the first two works, we have proposed two experimental schemes for the synthesis of two-dimensional topological lattices in ultra-cold atomic systems. In the third work, we describe the scheme of using polarized dipole Fermi gas to realize one-dimensional topological superconductors (Kitaev chains), and focus on the study of the interaction effect. In the first work, we propose an experimental scheme for the synthesis of topological nonmediocre magnetic lattices using magnetic pulse sequences based on phase lithography. The equivalent Hamiltonian generated by this scheme can be mapped to Haldane's topological old insulator model under adiabatic limit. By adjusting the magnetic field parameters, we can drive the lowest energy band of Hamiltonian to take place a topological phase transition between the topological Chen insulator and the topological mediocre insulator. The topological flat band can be realized near the phase transition point. In the second work, we propose an experimental scheme for the generation of luminous flux lattices with topologically nonmediocre band structures using amplitude modulated Raman lasers and RF magnetic fields. The topological properties of the minimum energy band of the time-free equivalent Hamiltonian synthesized by this scheme depend on the intensity of Raman laser and RF magnetic field. We investigate the energy bands of equivalent Hamiltonian and the corresponding aging numbers at different Raman laser and RF magnetic field intensities, and obtain the ground state phase diagram of the system under single filling. There are three different phases in the phase diagram: topological old insulator phase, normal insulator phase, and semi-metallic phase. This scheme can also achieve Haldane model, topological phase transition, and topological flat band. In the third work, we describe the scheme of one-dimensional interacting topological superconductors using polarized dipole Fermi gas. The energy spectrum of the system under interaction is calculated by strictly diagonalized numerical method, and the ground state diagram with the interaction intensity and chemical potential as parameters is obtained. There are five phases in the phase diagram: the insulator phase with one filling number, the vacuum phase with zero filling number, the Mott insulator phase with 1 / 2 filling number, the topological superconductor phase and the Luttinger liquid phase. The properties of different phases in the ground state are described by means of the ground state energy gap, the fidelity polarizability, the parity of the ground state population and the squeezing ratio of the ground state. We calculate the Majorana zero-mode wave function under the interaction, describe the entanglement properties of the ground state (entanglement spectrum, entanglement entropy, central charge), and prove the characteristics of the Luttinger liquid state element excited without energy gap by the finite scale method.
【学位授予单位】：清华大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O469
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