Space-time geometry of topological phases

The 2 + 1 dimensional lattice models of Levin and Wen (2005) [1] provide the most general known microscopic construction of topological phases of matter. Based heavily on the mathematical structure of category theory, many of the special properties of these models are not obvious. In the current paper, we present a geometrical space-time picture of the partition function of the Levin-Wen models which can be described as doubles (two copies with opposite chiralities) of underlying anyon theories. Our space-time picture describes the partition function as a knot invariant of a complicated link, where both the lattice variables of the microscopic Levin-Wen model and the terms of the Hamiltonian are represented as labeled strings of this link. This complicated link, previously studied in the mathematical literature, and known as Chain-Mail, can be related directly to known topological invariants of 3-manifolds such as the so-called Turaev-Viro invariant and the Witten-Reshitikhin-Turaev invariant. We further consider quasi-particle excitations of the Levin-Wen models and we see how they can be understood by adding additional strings to the Chain-Mail link representing quasi-particle world-lines. Our construction gives particularly important new insight into how a doubled theory arises from these microscopic models.     

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。     

声子晶体中的多重拓扑相

研究了圆环型波导依照蜂窝结构排列的声子晶体系统中的拓扑相变.利用晶格结构的点群对称性实现赝自旋,并在圆环中引入旋转气流来打破时间反演对称性.通过紧束缚近似模型计算的解析结果表明,没有引入气流时,调节几何参数,系统存在普通绝缘体和量子自旋霍尔效应绝缘体两个相;引入气流后,可以实现新的时间反演对称性破缺的量子自旋霍尔效应相,而增大气流强度,则可以实现量子反常霍尔效应相.这三个拓扑相可以通过自旋陈数来分类.通过有限元软件模拟了多个系统中边界态的传播,发现不同于量子自旋霍尔效应相,量子反常霍尔相系统的表面只支持一种自旋的边界态,并且它无需时间反演对称性保护.     

Appearance of topological phases in superconducting nanocircuits

We construct non-Abelian geometric transformations in superconducting nanocircuits, which resemble in properties the Aharonov-Bohm phase for an electron transported around a magnetic flux line. The effective magnetic fields can be strongly localized, and the path is traversed in the region where the energy separation between the states involved is at maximum, so that the adiabaticity condition is weakened. In particular, we present a scheme of topological charge pumping.     

Berry phases and zero-modes in toroidal topological insulator

An effective Hamiltonian describing the surface states of a toroidal topological insulator is obtained, and it is shown to support both bound-states and charged zero-modes. Actually, the spin connection induced by the toroidal curvature can be viewed as an position-dependent effective vector potential, which ultimately yields the zero-modes whose wave-functions harmonically oscillate around the toroidal surface. In addition, two distinct Berry phases are predicted to take place by the virtue of the toroidal topology.     

Transpose symmetry of the Jones matrix and topological phases

The transmission Jones matrix of an arbitrary stack of reciprocal plane-parallel plates that has been turned through 180 degrees about an axis in the plane of the stack is, in an appropriate basis, the transpose of the transmission matrix of the unturned slab with a change in the sign of the off-diagonal elements. We prove this convention-free result for the case where reflection at the interfaces can be ignored and use it to devise an experimental scheme to separate isotropic and topological phase changes in a reciprocal optical medium.     

Polarization of light and hopf fibration

A set of polarization states of quasi-monochromatic light is described geometrically in terms of the Hopf fibration. Several associated alternative polarization parametrizations are given explicitly, including the Stokes parameters.Presented at the International Conference Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 23–27, 1986.Based on a common work with J. Tolar [7].     

Strongly nonlinear topological phases of cascaded topoelectrical circuits

Circuits provide ideal platforms of topological phases and matter, yet the study of topological circuits in the strongly nonlinear regime, has been lacking. We propose and experimentally demonstrate strongly nonlinear topological phases and transitions in one-dimensional electrical circuits composed of nonlinear capacitors. Nonlinear topological interface modes arise on domain walls of the circuit lattices, whose topological phases are controlled by the amplitudes of nonlinear voltage waves. Experimentally measured topological transition amplitudes are in good agreement with those derived from nonlinear topological band theory. Our prototype paves the way towards flexible metamaterials with amplitude-controlled rich topological phases and is readily extendable to two and three-dimensional systems that allow novel applications.     

Polarization of diffusely scattered light

Journal of Applied Spectroscopy -     

Fermionic and bosonic scattering phases on a topological kink

A general approach to the scattering of fundamental fermions and bosons on a topological kink excitation is considered. An asymptotic LSZ-analysis for secondary quantized Heisenberg fields and kink motion is developed and some new results for the phases of one-particle matrix elements for the elastic scattering on the kink are derived.     

Aharonov-Casher和He-McKellar-Wilkens相位的对偶对称关系

本文首先对电磁理论中的对偶对称性以及对偶变换做了简要回顾.然后讨论了与电磁相互作用相联系的Aharonov-Casher和He-McKellar-Wilkens相位之间的对偶对称性.最后,在宇称不守恒但具有相对论不变性的条件下,给出了一般情况下描述Aharonov-Casher和He-McKellar-Wilkens相位之间对偶对称关系的拉格朗日量,从而建立了统一的、不依赖于模型的描述Aharonov-Casher和He-McKellar-Wilkens相位之间对偶对称关系的方法.     

能谷光子晶体与拓扑光传输

在传统光学原理框架下,高效光传输问题在集成光电子领域的发展受到了制约。人们希望从物理源头出发,提出新型原理机制或设计方法,来获得整体上的高保真光传输性能。这正好与近年兴起的拓扑光子学内涵相吻合。近年来,光子晶体和超构材料等多种电磁系统都被用于拓扑光子学的研究中,并受到了广泛关注。文章简要回顾拓扑光子学的发展历程,重点介绍能谷光子晶体的物理特性和最新研究进展,集中论述了电磁对偶能谷光子晶体的理论提出、能谷光子晶体分类与微波实验观测、硅基能谷光子晶体与光波段传输实现等方面。最后,将讨论该领域的未来,并展望其在微纳集成光子学领域的可能发展方向。     

On the stability of topological phases on a lattice

We study the stability of anyonic models on lattices to perturbations. We establish a cluster expansion for the energy of the perturbed models and use it to study the stability of the models to local perturbations. We show that the spectral gap is stable when the model is defined on a sphere, so that there is no ground state degeneracy. We then consider the toric code Hamiltonian on a torus with a class of abelian perturbations and show that it is stable when the torus directions are taken to infinity simultaneously, and is unstable when the thin torus limit is taken.     

Polarization squeezing in polarized light

It is shown that polarized light can be polarization squeezed only if it exhibits sub-Poissonian statistics with the Mandel's Q factor less than − 1/2.     

Polarization transformations of multimode light fields

The concept of P-quasispin is used as a framework for developing a formalism for polarization transformation by means of lossless polarization-changing optical elements for both classical and quantum multimode light fields. As an example, a classification of transformations of this kind is presented for two-mode biphoton fields that implement the information-theoretic concepts of qutrit and ququart (quantum systems in three-and four-dimensional Hilbert states, respectively). Original Russian Text ? V.P. Karassiov, S.P. Kulik, 2007, published in Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2007, Vol. 131, No. 1, pp. 37–53.     

Controllable simulation of topological phases and edge states with quantum walk

We simulate various topological phenomena in condense matter, such as formation of different topological phases, boundary and edge states, through two types of quantum walk with step-dependent coins. Particularly, we show that one-dimensional quantum walk with step-dependent coin simulates all types of topological phases in BDI family, as well as all types of boundary and edge states. In addition, we show that step-dependent coins provide the number of steps as a controlling factor over the simulations. In fact, with tuning number of steps, we can determine the occurrences of boundary, edge states and topological phases, their types and where they should be located. These two features make quantum walks versatile and highly controllable simulators of topological phases, boundary, edge states, and topological phase transitions. We also report on emergences of cell-like structures for simulated topological phenomena. Each cell contains all types of boundary (edge) states and topological phases of BDI family.     

Polarization invariance and biphoton coherent states of light

A new classification of polarization states of quantum light fields is given using the concept of the polarization (P) spin due to the polarization gauge SU_p(2) invariance of free light fields [I]. Generalized coherent states (GCS) asNociated with P-scalar biphotons are discussed. We also point out some applications of the results in the optical communication theory.Presented at the International Workshop on Squeezed and Correlated States in Quantum Optics, Moscow, December 3–7, 1990.