拓扑相和拓扑相变的量子模拟

随着拓扑相和拓扑材料的发现,拓扑已经从数学概念变成现代凝聚态物理学一个重要的前沿方向。尽管越来越多的拓扑材料被预言,在人造可控量子体系中进行拓扑量子模拟仍会对材料的理解和制备起到极大的促进作用。文章简单总结了基于冷原子和超导量子比特系统开展拓扑量子模拟的进展。介绍了这两种量子系统的特点,以及相应的拓扑量子模拟实验方法,还分析了这两种体系在实验手段和物理原理上的联系。     

非厄米局域拓扑指标的动力学特性

非厄米拓扑系统的拓扑不变量可以由定义在双正交基下的局域拓扑指标刻画.不同于厄米体系,非厄米局域拓扑指标在动力学过程中的传播和演化目前还未见文献讨论.本文研究非厄米拓扑体系局域拓扑指标的动力学特性,重点关注淬火过程中,局域拓扑指标由边界向体内的传播.结果表明,当淬火前后的体系拓扑性质不同时,系统中存在局域拓扑指标的流动,其流速与体系群速度相关,但具体形式与相应厄米体系不同.以3个具体模型为例,通过数值计算说明了这一结论.其中,对于特定具有非厄米趋肤效应的模型,可以发现局域拓扑指标的流速上限与广义布里渊区中的群速度直接相关.但这一关系在其他非厄米模型中则需要修正,其更普适的形式有待进一步研究.本文的结果揭示了非厄米体系中局域拓扑指标传播的复杂性,是进一步理解非厄米局域拓扑指标动力学行为的基础.     

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.     

探究弦球链系统的拓扑不变量

周期性弦球链体系作为典型的声子晶体体系,其能带结构已得到了广泛而深入的研究.在实际观测体系能谱的过程中,会探测到一类特殊的能量本征态——边缘态(能量处在带隙间,且波函数局域在体系边缘的态),同时观察到其存在具有一定的鲁棒性.由于实验上观测到的弦球链边缘态的性质与电子体系中拓扑绝缘体的边缘态性质的相似性,可以利用同一套能带拓扑的语言研究弦球链体系.本文通过数值计算能带的拓扑不变量,揭示了弦球链体系非平庸的拓扑性质,从而证明了实验上探测到的边缘态是拓扑保护的边缘态.基于数值计算的结果,讨论了体系的拓扑相变与边缘态的输运性质     

一维化学势调制的p波超导体中的拓扑量子相变

本文研究了一维公度势和非公度势调制下的p波超导量子线系统的拓扑相变.在公度势调制下,通过计算Z2拓扑不变量确定系统的相图,指出系统的拓扑相变强烈地依赖于调制参数α和相移δ.在非公度势调制下,以α=(√5-1)/2,δ=0为例,计算系统的低能激发谱、Z2拓扑不变量以及逆参与率等,发现p波配对强度△∈(0,0.33)时,系统存在拓扑非平庸超导相,拓扑平庸超导相和拓扑平庸局域相的转变.而当p波配对强度△>0.33时,系统存在拓扑非平庸超导相和拓扑平庸局域相的转变.     

费米6Li冷原子装载动力学的研究

我们用简单的系统实现了6 Li费米原子的冷却及俘获,研究了磁光阱中冷原子的装载动力学.由于其质量小和反冲动量大等特点,装载、冷却及俘获过程和其他的碱金属原子具有极大的不同.我们测量了装载率、单体碰撞损失率和原子数与温度的关系.基于气体动能和原子碰撞散射的理论计算来解释实验的测量结果.实现的长寿命6Li冷原子对将来研究超冷费米原子的量子简并及其强相互作用具有重要的意义.     

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.     

瞬态涡旋动力学与非平衡体系中的异常核现象

根据实验现象和已发表的数据,对电解过程中的尖端效应、磁自收缩现象、阴极表面电化学双层的高能集中、极化核聚变的产生进行了分析研究.利用CR 39固体径迹探测器记录到电化学系统中高度集中而且准直的10MeV以上的异常高能带电粒子.提出了涡旋动力学理论解释电化学放电过程中的异常现象———过剩热和非平衡系统中的异常核现象. The tip effect, magnetism self-pinch phenomena, high energy concentration on the cathode surface, electrochemical double layer, and polarized nucleus fusion in the process of electrolysis have been studied and discussed. The high concentrated and straight charged particles with energy above 10 MeV in (electrochemistry) systems were recorded by CR-39 solid trace detector. The hypothesis of vortex dynamics is proposed for explaining the peculiarities of excess heat and anomalous nucleus phenomena...     

强激光场下原子超快动力学过程中的能量交换

利用三维经典系综模型,研究了整个系综两电子(Ar原子为例)从激光场吸收的能量对激光参数(波长、激光强度和椭偏率)的依赖关系.结果显示,当激光强度固定,波长增加时,整个系综两电子从激光场吸收的能量整体呈上升趋势,但不同强度下趋势略有差异.在较低强度时整个系综两电子从激光场吸收的能量对波长的依赖关系呈现持续平稳增加的趋势,在较高强度时呈现先缓慢减小再快速增大的趋势.对强度的依赖关系在不同波长时呈现两个有趣的交叉点.对椭偏率的依赖关系在较低强度时呈现先逐渐减小再缓慢增大的趋势;在中等强度时呈现一个“阶梯型”即先缓慢增大再逐渐减小最后缓慢增大;在更高强度时呈现先逐渐增大再逐渐减小的趋势.为了解释整个系综两电子从激光场吸收的能量对激光参数的依赖关系,把整个系综的动力学过程分为双电离、单电离、受挫单电离和受挫双电离4种通道.然后分析各个通道的特征及其如何主导整个系综两电子从激光场吸收的能量的变化趋势.分析结果表明,整个系综两电子从激光场吸收的能量对波长、激光强度和椭偏率的依赖均是由于某种通道主导整个系综两电子从激光场吸收的能量的结果.     

铯47D精细能级超冷里德堡原子自由演化的动力学研究

用连续窄线宽激光器将超冷铯里德堡原子分别激发到47D_3/2, 47D_5/2精细态, 观察了处于里德堡精细态的铯原子向超冷铯等离子体自由演化的过程, 详细对比了不同精细态的铯里德堡原子预电离时间、电离速率以及等离子体的转化效率. 将里德堡原子快速转化为等离子体的过程解释为局域势阱内由预电离产生的电子与里德堡原子的快速碰撞导致的雪崩电离.     

Static and dynamic properties of polymer brush with topological ring structures: Molecular dynamic simulation

By defining a topological constraint value(rn),the static and dynamic properties of a polymer brush composed of moderate or short chains with different topological ring structures are studied using molecular dynamics simulation,and a comparison with those of linear polymer brush is also made.For the center-of-mass height of the ring polymer brush scaled by chain length h~N~v,there is no significant difference of exponent from that of a linear brush in the small topological constraint regime.However,as the topological constraint becomes stronger,one obtains a smaller exponent.It is found that there exists a master scaling power law of the total stretching energy scaled by chain length N for moderate chain length regime,F_(ene)~Np~v,for ring polymer brushes,but with a larger exponent v than 5/6,indicating an influence of topological constraint to the dynamic properties of the system.A topological invariant of free energy scaled by(c)~(5/4) is found.     

Z2拓扑不变量与拓扑绝缘体

文章回顾了几种Z2拓扑数的计算方法,并详细介绍了一种用非阿贝尔贝里联络表示绝缘体Z2不变量的计算方法.这种方法可以确定出一般能带绝缘体的拓扑性质,而不需要限定波函数的规范.利用这种新方法,文章作者计算了二维石墨烯(graphene)系统的Z2拓扑数,得到了和以前研究相一致的结论.     

Z_2拓扑不变量与拓扑绝缘体

文章回顾了几种Z2拓扑数的计算方法,并详细介绍了一种用非阿贝尔贝里联络表示绝缘体Z2不变量的计算方法.这种方法可以确定出一般能带绝缘体的拓扑性质,而不需要限定波函数的规范.利用这种新方法,文章作者计算了二维石墨烯(graphene)系统的Z2拓扑数,得到了和以前研究相一致的结论.     

Interplay of the Staggered and Three-Body Interaction Potentials on the Quantum Phases of a Spin-1 Ultracold Atom in an Optical Lattice

The interplay of the staggered and the three-body interaction potentials on the quantum phases of a spin-1 Bose Hubbard model using a mean field approximation (MFA) is studied. In the antiferromagnetic (AF) case, a smaller value of the staggered potential (SP) results in the charge and the spin density wave ordering along with the Mott insulator (MI) and the staggered superfluid (SSF) phases. While the competition between two types of the potential leads to the stabilization of the higher order MI and charge density wave (CDW) phases with increasing three-body interaction strength. Further, the spin eigenvalue and nematic order parameters are calculated to scrutinize the spin singlet-nematic formation in the MI and the CDW phases and spin population fractions to analyze the nature of the SSF phase. A signature of the spin density wave (SDW) pattern is also observed in the gapped phase lobes. In case of a purely three-body interaction, the third and higher order insulating lobes become dominant with increasing staggered potential strength. Subsequently, all MFA phase diagrams are then nicely corroborated with the analytical results obtained using a perturbative expansion corresponding to the AF and ferromagnetic cases.     

Complex energy plane and topological invariant in non-Hermitian systems

Non-Hermitian systems as theoretical models of open or dissipative systems exhibit rich novel physical properties and fundamental issues in condensed matter physics. We propose a generalized local–global correspondence between the pseudo-boundary states in the complex energy plane and topological invariants of quantum states. We find that the patterns of the pseudo-boundary states in the complex energy plane mapped to the Brillouin zone are topological invariants against the parameter deformation. We demonstrate this approach by the non-Hermitian Chern insulator model. We give the consistent topological phases obtained from the Chern number and vorticity. We also find some novel topological invariants embedded in the topological phases of the Chern insulator model, which enrich the phase diagram of the non-Hermitian Chern insulators model beyond that predicted by the Chern number and vorticity. We also propose a generalized vorticity and its flipping index to understand physics behind this novel local–global correspondence and discuss the relationships between the local–global correspondence and the Chern number as well as the transformation between the Brillouin zone and the complex energy plane. These novel approaches provide insights to how topological invariants may be obtained from local information as well as the global property of quantum states, which is expected to be applicable in more generic non-Hermitian systems.     

基于光晶格的超冷原子量子模拟

文章从超冷原子研究的视角出发,回顾了用“从下到上”的方案来开展量子模拟研究的历史。超冷原子作为宏观量子态,各个自由度精确可控,是量子模拟的绝佳平台。光晶格将冷原子物理和凝聚态物理融合起来,是其中最重要的技术之一,为超冷原子量子模拟提供了一个扎实的落脚点。近年来,关于拓扑量子模拟的研究日益兴起,成为超冷原子量子模拟新的重要方向。文章介绍这方面近期的一些工作进展。最后分享作者对超冷原子量子模拟的一些思考。     

Dissipation-induced topological phase transition and periodic-driving-induced photonic topological state transfer in a small optomechanical lattice

We propose a scheme to investigate the topological phase transition and the topological state transfer based on the small optomechanical lattice under the realistic parameters regime.We find that the optomechanical lattice can be equivalent to a topologically nontrivial Su-Schrieffer Heeger(SSH)model via designing the effective optomechanical coupling.Especially,the optomechanical lattice experiences the phase transition between topologically nontrivial SSH phase and topologically trivial SSH phase by controlling the decay of the cavity field and the opto mechanical coupling.We stress that the to pological phase transition is mainly induced by the decay of the cavity field,which is counter-intuitive since the dissipation is usually detrimental to the system.Also,we investigate the photonic state transfer between the two cavity fields via the topologically protected edge channel based on the small optomechanical lattice.We find that the quantum st ate transfer assisted by the topological zero energy mode can be achieved via implying the external lasers with the periodical driving amplitudes into the cavity fields.Our scheme provides the fundamental and the insightful explanations towards the mapping of the photonic topological insulator based on the micro-nano optomechanical quantum optical platform.     

Novel Quantum Phases of Ultracold Bosonic Atoms in Honeycomb Optical Lattice

We study the quantum phase transition of ultracold atoms in the honeycomb optical lattice. The Hamiltonian of ultracold bosonic atoms in the honeycomb optical lattice is derived. We take the mean-field approximation and further solve the Hamiltonian with the numerical diagonalization method. We obtain the phase diagram and find that the Mort-insulator （MI）, density wave （DW） and modulated superfluid （MS） phases appear. Furthermore, the phase diagram is analyzed according to the order parameter and the average number of particles.     

铁基超导中拓扑量子态研究进展

铁基超导体和拓扑量子材料是近年来凝聚态物理两个重要的前沿研究方向.铁基超导体中是否能衍生出非平庸的拓扑现象是一个非常有意义的问题.本文从晶体对称性、布里渊区高对称点附近的有效模型以及自旋轨道耦合相互作用三个方面具体分析了铁基超导的电子结构的基本特点.在此基础上,重点阐述铁基超导的正常态、临近超导的长程有序态以及超导态中非平庸的拓扑量子态是如何衍生的;具体介绍了相关的理论模型以及结果,回顾了相关的实验进展,展望了该领域的发展前景.