Rashba自旋轨道耦合下square-octagon晶格的拓扑相变

本文研究了各向同性square-octagon晶格在内禀自旋轨道耦合、Rashba自旋轨道耦合和交换场作用下的拓扑相变,同时引入陈数和自旋陈数对系统进行拓扑分类.系统在自旋轨道耦合和交换场的影响下会出现许多拓扑非平庸态,包括时间反演对称破缺的量子自旋霍尔态和量子反常霍尔态.特别的是,在时间反演对称破缺的量子自旋霍尔效应中,无能隙螺旋边缘态依然能够完好存在.调节交换场或者填充因子的大小会导致系统发生从时间反演对称破缺的量子自旋霍尔态到自旋过滤的量子反常霍尔态的拓扑相变.边缘态能谱和自旋谱的性质与陈数和自旋陈数的拓扑刻画完全一致.这些研究成果为自旋量子操控提供了一个有趣的途径.     

超冷原子动量光晶格中的非线性拓扑泵浦

在拓扑系统中,探索相互作用引起的新奇的拓扑泵浦现象日益受到人们的关注,其中包括由相互作用诱导的非线性拓扑泵浦.本文提出可以利用超冷原子动量光晶格系统,有效地模拟一维非线性的非对角Aubry-André-Harper (AAH)模型,研究非线性拓扑泵浦的实验方案.首先,通过数值方法计算了一维非对角AAH模型的非线性能带结构随相互作用强度的变化,得到了非线性系统的孤子态解.然后,分析了不同相互作用强度下孤子态的拓扑输运,发现其质心的移动距离具有量子化的输运特征,由所占据能带的陈数决定,并讨论了非线性拓扑泵浦对相互作用符号的依赖性.同时还计算了在不同相互作用强度下,系统最低能带和最高能带对应陈数的分布.最后,基于⁷Li原子的动量光晶格实验系统,提出了一个非线性拓扑泵浦方案.本文构造了一种近似于孤子态分布的初始态并演示了其动力学演化过程,并分析了绝热演化条件对泵浦过程的影响.结果表明,在动量晶格系统中演示非线性拓扑泵浦具有可行性.本文的工作为在超冷原子系统中研究非线性拓扑泵浦提供了一个可行的途径,有助于进一步探测非线性引起的拓扑相变和边界效应.     

时间反演对称性破缺系统中的拓扑零能模

Su-Schreiffer-Heeger模型预测了在一维周期晶格的边缘处可能出现零维的拓扑零能模,其能量本征值总是出现在能隙的正中间.本文以半导体微腔阵列中光子和激子在强耦合情况下形成的准粒子为例,通过准粒子的自旋轨道耦合与Zeeman效应,研究了时间反演对称性破缺对拓扑零能模的影响.发现拓扑零能模的能量本征值可以随着自旋轨道耦合强度的变化在整个带隙内移动,自旋相反的模式移动方向相反;在二维微腔阵列中发现了沿着晶格边缘移动的拓扑零能模,提出了一维零能模的概念.由于时间反演对称性的破缺,这种一维拓扑零能模解除了在相反传输方向上的能级的简并,从而在传输过程中出现极强的绕过障碍物的能力.     

二维范德瓦耳斯半导体莫尔超晶格实验研究进展

在二维范德瓦耳斯材料中,可以通过转角及晶格失配构造周期性的莫尔超晶格.自从实验上在“魔角”石墨烯系统中观察到关联绝缘体态和超导电性以来,利用各种二维范德瓦耳斯材料构造莫尔超晶格并研究其中的新奇量子物态成为了凝聚态物理研究的热点和前沿问题.本文主要综述了最近几年在二维半导体过渡金属硫族化合物莫尔超晶格系统中的相关实验进展.在该系统中实现电子“平带”不依赖于特定魔角,实验上,一系列的关联电子物态和拓扑电子物态被相继发现和证实.进一步的理论和实验研究有望在该系统中揭示更多的受电子关联作用和拓扑物理共同支配的新奇量子物态.     

一维锯齿晶格中费米气体的边界态

本文研究了一维锯齿晶格中自旋轨道耦合与Zeeman场驱动的双组分费米气体的拓扑性质。我们理论计算了系统的能谱,利用矩阵乘积态(MPS)数值研究了多个物理量(系统的边界态、冯诺依曼熵、纠缠谱和激发能隙),并据此分析了系统的拓扑性质。发现在填充因子为半填充时,边界态的存在可以用来表征系统的拓扑性。而填充因子为1/4(或3/4)时,虽然系统存在边界态,但该系统并不具备一般拓扑态的其他特征,该类边界态不能用于表征拓扑态。     

人工带隙材料的拓扑性质

近年来,人工带隙材料(如声子晶体和光子晶体)由于其优异的性能,已成为新一代智能材料的研究焦点.另一方面,材料拓扑学由凝聚态物理领域逐渐延伸到其他粒子或准粒子系统,而研究人工带隙材料的拓扑性质更是受到人们的广泛关注,其特有的鲁棒边界态,具有缺陷免疫、背散射抑制和自旋轨道锁定的传输等特性,潜在应用前景巨大.本文简要介绍拓扑材料特有的鲁棒边界态的物理图像及其物理意义,并列举诸如光/声量子霍尔效应、量子自旋霍尔效应、Floquet拓扑绝缘体等相关工作;利用Dirac方程,从原理上分析光/声拓扑性质的由来;最后对相关领域的发展方向和应用前景进行了相应的讨论.     

金属多层膜与超晶格中的自旋波及布里渊散射研究

评述了近年来迅速发展的金属多层膜与超晶格中的磁性激发理论和实验。着重于借助 布里渊散射在双层、多层膜中新发现的自旋波模式。首先介绍了磁性介质中自旋波模式的 一般理论,比较了观测自旋波的实验方法,然后,对单层、双层、多层膜中的理论结果作 一总结,并与实验进行了比较,最后讨论了一种新的磁性超晶格——反平行磁化超晶格中 的自旋波。     

基于结构反转二维光子晶体的拓扑相变及拓扑边界态的构建

构建了二维六角蜂窝晶格的两种结构,让散射体和基体材料反转.由于特有的点群对称,该晶格在布里渊区中心具有类比电子体系的p轨道和d轨道.在散射体和基体反转的两种结构中, p轨道和d轨道也直接实现了反转.定量分析了产生轨道反转的原因来自于低频局域共振产生空气带和介质带的反转.通过p轨道和d轨道的宇称特性,构建了类比电子体系量子自旋霍尔效应的赝自旋态.通过Γ点处有效哈密顿量的分析,揭示轨道反转导致的拓扑相变.通过结构的优化,构建了基于赝自旋的拓扑边界态.电磁波仿真模拟和能流矢量分析证明了结构具有电子体系量子自旋霍尔效应的特性,即自旋与传播方向锁定和拓扑保护.结果也证明经典波量子自旋霍尔效应的实现可以不经历带隙关闭的过程.与同类型的研究相比较,本文的结构不需要晶格的缩放,具有设计简单、带隙宽和边界态局域性较强的特点.     

一维超冷原子动量光晶格中的手征对称性破缺拓扑相

对称性在理解物质的拓扑态方面具有关键作用.过去人们认为手征对称性保证了一维晶格的量子化Zak相位及其对应的非平庸拓扑相.本文展现了在一维手征对称性破缺的情况下,晶格系统仍具有量子化Zak相位和非平庸拓扑相.具体而言,在超冷原子动量晶格系统中有效地模拟了一个链长为26、手征对称性破缺的Zigzag模型,其中相等的次近邻耦合强度能够在保留空间反演对称性的同时破坏手征对称性.通过测量原子的时间平均波包位移来获得系统的拓扑不变量,并得到了其对应的量子化的Zak相位.此外,还观测到系统随着最近邻耦合强度比例的变化会从非平庸拓扑相转变为平庸拓扑相.本文不仅为对称性及拓扑相的相关研究提供了一个完全可控的平台,还可以通过控制格点间耦合强度和原子间相互作用,探索例如Tasaki, Aharonov-Bohm caging模型中的平带拓扑以及引入相互作用研究的非线性拓扑现象.     

自旋轨道耦合玻色爱因斯坦凝聚体中的拉曼耦合强度

对玻色爱因斯坦凝聚中拉曼跃迁的拉比频率和耦合强度进行了实验研究,拉比频率是光与原子相互作用中的一个重要参量,用于衡量原子与光场之间耦合强度的大小,而拉曼跃迁耦合强度是自旋轨道耦合实验中的一个重要参数。研究了不同拉曼光频率失谐下,87 Rb在F=1时的超精细塞曼子能态|1,0〉和|1,1〉间的拉曼跃迁拉比振荡。在800nm的拉曼光作用下,观测到超精细态F=2的5个塞曼能态间同时耦合的拉比振荡。该工作有助于87 Rb自旋轨道耦合实验中参数的优化选择。     

Topological superfluid in a two-dimensional polarized Fermi gas with spin-orbit coupling and adiabatic rotation

We study the properties of superfluid in a two-dimensional(2 D) polarized Fermi gas with spin–orbit coupling and adiabatic rotation which are trapped in a harmonic potential. Due to the competition between polarization, spin–orbit coupling, and adiabatic rotation, the Fermi gas exhibits many intriguing phenomena. By using the Bardeen–Cooper–Schrieffer(BCS) mean-field method with local density approximation, we investigate the dependence of order parameter solution on the spin–orbit coupling strength and the rotation velocity. The energy spectra with different rotation velocities are studied in detail. Besides, the conditions for the zero-energy Majorana fermions in topological superfluid phase to be observed are obtained. By investigating distributions of number density, we find that the rotation has opposite effect on the distribution of number density with different spins, which leads to the enhancement of the polarization of Fermi gas. Here,we focus on the region of BCS pairing and ignore the Fulde–Ferrell–Larkin–Ovchinnikov state.     

Surface Majorana cone of the topological superfluid 3He B phase

Topological superfluids and superconductors have been theoretically proposed, and it is now necessary to experimentally confirm their existence. Superfluid ³He should be the ideal test subject for topological theories because its bulk state is established to be that of a spin-triplet p-wave superfluid. Surface Andreev bound states of superfluid ³He were investigated by transverse acoustic impedance measurements and their linear dispersion was confirmed on a highly specular wall. The superfluid ³He B phase was found to be a topological superfluid showing bulk–edge correspondence and a surface Majorana cone was confirmed on the surface. Possible manifestations of the Majorana nature of the surface states are discussed.     

Energetic and dynamical instability of spin–orbit coupled Bose–Einstein condensate in a deep optical lattice

We investigate the energetic and dynamical instability of spin–orbit coupled Bose–Einstein condensate in a deep optical lattice via a tight-binding model. The stability phase diagram is completely revealed in full parameter space, while the dependence of superfluidity on the dispersion relation is illustrated explicitly. In the absence of spin–orbit coupling, the superfluidity only exists in the center of the Brillouin zone. However, the combination of spin–orbit coupling, Zeeman field, nonlinearity and optical lattice potential can modify the dispersion relation of the system, and change the position of Brillouin zone for generating the superfluidity. Thus, the superfluidity can appear in either the center or the other position of the Brillouin zone. Namely, in the center of the Brillouin zone, the system is either superfluid or Landau unstable, which depends on the momentum of the lowest energy. Therefore, the superfluidity can occur at optional position of the Brillouin zone by elaborating spin–orbit coupling, Zeeman splitting, nonlinearity and optical lattice potential. For the linear case, the system is always dynamically stable, however, the nonlinearity can induce the dynamical instability, and also expand the superfluid region. These predicted results can provide a theoretical evidence for exploring the superfluidity of the system experimentally.     

Some topological states in one-dimensional cold atomic systems

Ultracold atoms trapped in optical lattices nowadays have been widely used to mimic various models from condensed-matter physics. Recently, many great experimental progresses have been achieved for producing artificial magnetic field and spin–orbit coupling in cold atomic systems, which turn these systems into a new platform for simulating topological states. In this paper, we give a review focusing on quantum simulation of topologically protected soliton modes and topological insulators in one-dimensional cold atomic system. Firstly, the recent achievements towards quantum simulation of one-dimensional models with topological non-trivial states are reviewed, including the celebrated Jackiw–Rebbi model and Su–Schrieffer–Heeger model. Then, we will introduce a dimensional reduction method for systematically constructing high dimensional topological states in lower dimensional models and review its applications on simulating two-dimensional topological insulators in one-dimensional optical superlattices.     

Chiral p-wave pairing of ultracold fermionic atoms due to a quadratic band touching

We study the superfuild ground state of ultracold fermions in optical lattices with a quadratic band touching. Examples are a checkerboard lattice around half filling and a kagome lattice above one third filling. Instead of pairing between spin states, here we focus on pairing interactions between different orbital states. We find that our systems have only odd-parity(orbital) pairing instability while the singlet(orbital) pairing instability vanishes thanks to the quadratic band touching. In the mean field level, the ground state is found to be a chiral p-wave pairing superfluid(mixed with finite f-wave pairing order-parameters) which supports Majorana fermions.     

Topological superfluid in one-dimensional ultracold atomic system with spin-orbit coupling

We propose a one-dimensional Hamiltonian H _1D which supports Majorana fermions when d _{x² ? y²}-wave superfluid appears in the ultracold atomic system and obtain the phase diagrams both for the time-reversal-invariant (TRI) case and time-reversal-symmetry-breaking (TRSB) case. From the phase diagrams, we find that the Majorana doublets and the single Majorana fermions exist in the topological superfluid (TSF) regions for the TRI case and the TRSB case, respectively, and we can reach these regions by tuning the chemical potential μ and spin-orbit coupling α _R . Importantly, the spin-orbit coupling has been realized in ultracold atoms by the recent experimental achievement of synthetic gauge field, therefore, our one-dimensional ultra-cold atomic system described by H _1D is a promising platform to find the mysterious Majorana fermions.     

Spin and Majorana polarization in topological superconducting wires

We study a one-dimensional wire with strong Rashba and Dresselhaus spin-orbit coupling (SOC), which supports Majorana fermions when subject to a Zeeman magnetic field and in the proximity of a superconductor. Using both analytical and numerical techniques we calculate the electronic spin texture of the Majorana end states. We find that the spin polarization of these states depends on the relative magnitude of the Rashba and Dresselhaus SOC components. Moreover, we define and calculate a local "Majorana polarization" and "Majorana density" and argue that they can be used as order parameters to characterize the topological transition between the trivial system and the system exhibiting Majorana bound modes. We find that the local Majorana polarization is correlated to the transverse spin polarization, and we propose to test the presence of Majorana fermions in a 1D system by a spin-polarized density of states measurement.     

Topological phase transition in anisotropic square-octagon lattice with spin–orbit coupling and exchange field

We investigate the topological phase transitions in an anisotropic square-octagon lattice in the presence of spin–orbit coupling and exchange field. On the basis of the Chern number and spin Chern number, we find a number of topologically distinct phases with tuning the exchange field, including time-reversal-symmetry-broken quantum spin Hall phases, quantum anomalous Hall phases and a topologically trivial phase. Particularly, we observe a coexistent state of both the quantum spin Hall effect and quantum anomalous Hall effect. Besides, by adjusting the exchange filed, we find the phase transition from time-reversal-symmetry-broken quantum spin Hall phase to spin-imbalanced and spin-polarized quantum anomalous Hall phases, providing an opportunity for quantum spin manipulation. The bulk band gap closes when topological phase transitions occur between different topological phases. Furthermore, the energy and spin spectra of the edge states corresponding to different topological phases are consistent with the topological characterization based on the Chern and spin Chern numbers.     

All-optical scheme for detecting the possible Majorana signature based on QD and nanomechanical resonator systems

Majorana fermions(MFs) are exotic particles that are their own anti-particles. Currently, the search for MFs occurring as quasiparticle excitations in condensed matter systems has attracted widespread interest, because of their importance in fundamental physics and potential applications in topological quantum computation based on solid-state devices. Motivated by recent experimental progress towards the detection and manipulation of MFs in hybrid semiconductor/superconductor heterostructures, in this review, we present a novel proposal to probe MFs in all-optical domain. We introduce a single quantum dot(QD), a hybrid quantum dot-nanomechanical resonators(QD-NR) system, and a carbon nanotube(CNT) resonator implanted in a single electron spin system with optical pump-probe technology to detect MFs, respectively. With this scheme, a possible Majorana signature is investigated via the probe absorption spectrum and nonlinear optical Kerr effect, and the coupling strength between MFs and the QD or the single electron spin is also determined. In the hybrid QD-NR system, vibration of the NR will enhance the nonlinear optical effect, which makes the MFs more sensitive for detection. In the CNT resonator with a single electron, the single electron spin can be considered as a sensitive probe, and the CNT resonator behaved as a phonon cavity is robust for detecting of MFs. This optical scheme will provide another method for the detection MFs and will open the door for new applications ranging from robust manipulation of MFs to quantum information processing based on MFs.     

Probing non-abelian statistics of Majorana fermions in ultracold atomic superfluid

We propose an experiment to directly probe the non-abelian statistics of Majorana fermions by braiding them in an s-wave superfluid of ultracold atoms. We show that different orders of braiding operations give orthogonal output states that can be distinguished through Raman spectroscopy. Realization of Majorana states in an s-wave superfluid requires strong spin-orbital coupling and a controllable Zeeman field in the perpendicular direction. We present a simple laser configuration to generate the artificial spin-orbital coupling and the required Zeeman field in the dark-state subspace.