Topological Vortices in Superfluid Films

We study the topological structure of the vortex system in a superfluid film. Explicit expressions for the vortex density and velocity field as functions of the superfluid order parameter are derived. The evolution of vortices is also studied from the topological properties of the superfluid order parameter field.     

Topological Vortices in Superfluid Films

We study the topological structure of the vortex system in a superfiuid film. Explicit expressions for the vortex density and velocity field as functions of the superfluid order parameter are derived. The evolution of vortices is also studied from the topological properties of the superfluid order parameter field.     

Vortex pinning with non-spherical nuclei

We investigate the pinning energies of superfluid vortex lines inside the inner crust of a neutron star taking into account the presence of nuclei with non-spherical shapes. It is found that vortex lines pin to the unusual nuclei with an energy larger respect to the spherical case.Communicated by: B. Povh     

Spatial structure of a vortex in low density neutron matter

We study in a fully self-consistent approach the structure of a vortex in low density superfluid neutron matter. We determine that the matter density profile of a vortex shows a significant depletion in the region of the core, a feature never reported for a vortex state in a Fermi superfluid.     

Vortex lines in a ferromagnetic spin-triplet superconductor

Based on Duan's topological current theory, we show that in a ferromagnetic spin-triplet superconductor there is a topological defect of string structures which can be interpreted as vortex lines. Such defects are different from the Abrikosov vortices in one-component condensate systems. We investigate the inner topological structure of the vortex lines. The topological charge density, velocity, and topological current of the vortex lines can all be expressed in terms of δ function, which indicates that the vortices can only arise from the zero points of an order parameter field. The topological charges of vortex lines are quantized in terms of the Hopf indices and Brouwer degrees of φ-mapping. The divergence of the self-induced magnetic field can be rigorously determined by the corresponding order parameter fields and its expression also takes the form of a δ-like function. Finally, based on the implicit function theorem and the Taylor expansion, we conduct detailed studies on the bifurcation of vortex topological current and find different directions of the bifurcation.     

Vortices in He II,current algebras and quantum knots

A canonical quantization scheme is developed for vertices in superfluid He II, using Dirac's technique for constrained hamiltonian systems. Quantization introduces in the theory in natural way the structure of the infinite Lie algebra of incompressible flows. We argue that all the topological invariants of the vortex, considered as a knot, can be regarded as observables of the system. Finally unitary representations of measure preserving flows on R³ and current algebra are discussed.     

Nodal Topological Phases in s-wave Superfluid of Ultracold Fermionic Gases

The gapless Weyl superfluid has been widely studied in the three-dimensional ultracold fermionic superfluid.In contrast to Weyl superfluid, there exists another kind of gapless superfluid with topologically protected nodal lines,which can be regarded as the superfluid counterpart of nodal line semimetal in the condensed matter physics, just as Weyl superfluid with Weyl semimetal. In this paper we study the ground states of the cold fermionic gases in cubic optical lattices with one-dimensional spin-orbit coupling and transverse Zeeman field and map out the topological phase diagram of the system. We demonstrate that in addition to a fully gapped topologically trivial phase, some different nodal line superfluid phases appear when the Zeeman field is adjusted. The presence of topologically stable nodal lines implies the dispersionless zero-energy flat band in a finite region of the surface Brillouin zone. Experimentally these nodal line superfluid states can be detected via the momentum-resolved radio-frequency spectroscopy. The nodal line topological superfluid provide fertile grounds for exploring exotic quantum matters in the context of ultracold atoms.     

Effective lagrangian and topological interactions in supersolids

We construct a low-energy effective Lagrangian describing zero temperature supersolids. Galilean invariance imposes strict constraints on the form of the effective Lagrangian. We identify a topological term in the Lagrangian that couples superfluid and crystalline modes. For small superfluid fractions, this interaction term is dominant in problems involving defects. As an illustration, we compute the differential cross section of scatterings of low-energy transverse elastic phonons by a superfluid vortex. The result is model independent.     

超冷原子中拓扑超流的发展现状

拓扑超流态是一种奇异物质态,它的内部受能隙保护,而在其系统边缘却可以容纳无能隙的Majorana 费米子。由于该粒子满足非阿贝尔统计,并且受拓扑保护具有良好的稳定性,用它 们携带量子化的信息,可以用于拓扑量子计算的研究。近年来,理论工作预测了各类系统中可能 存在的拓扑超流态。我们首先介绍了在各类光晶格模型中的拓扑超流, 光晶格的超冷原子具有良 好的可控性与普适性,是实现拓扑超流的理想模型系统。接下来我们介绍了自旋轨道耦合调控下 的拓扑超流,自旋轨道耦合效应是诱导拓扑相的重要条件,并且人们已经在实验上合成了人工自 旋轨道耦合,这为实验上观测拓扑超流取得了突破性的进展。随着近年来实验技术的提高,曾经 难以在实验中观测的,被人们所忽略的拓扑Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) 超流相也 成为了人们研究的热点,因此我们接下来介绍了拓扑的FFLO 超流。此外,我们还介绍了拓扑超 流其他方面的进展,包括孤子引诱的拓扑超流、三组分的拓扑超流、大陈数的拓扑超流以及拓扑 超流临界温度的提高。在实验中,如何检测与实现拓扑超流,是其研究的目的及意义所在,因 此我们在文章的最后介绍了拓扑超流的识别与实现。     

Vortex Lines and Monopoles in Electrically Conducting Plasmas

Based on the φ-mapping topological current theory and the decomposition of gauge potential theory, the vortex lines and the monopoles in electrically conducting plasmas are studied. It is pointed out that these two topological structures respectively inhere in two-dimensional and three-dimensional topological currents, which can be derived from the same topological term n^→·（Эin^→×Эjn^→）, and both these topological structures axe characterized by the φ-mapping topological numbers-Hopf indices and Brouwer degrees. Furthermore, the spatial bifurcation of vortex lines and the generation and annihilation of monopoles are also discussed. At last, we point out that the Hopf invaxiant is a proper topological invaxiant to describe the knotted solitons.     

Topological Structure of Knotted Vortex Lines in Liquid Crystals

In this paper, a novel decomposition expression for the U（1） gauge field in liquid crystals （LCs） is derived. Using this decomposition expression and the b-mapping topological current theory, we investigate the topological structure of the vortex lines in LCs in detail. A topological invariant, i.e., the Chern-Simons （CS） action for the knotted vortex lines is presented, and the CS action is shown to be the total sum of all the self-linking and linking numbers of the knot family. Moreover, it is pointed out that the CS action is preserved in the branch processes of the knotted vortex lines.     

Topological aspect of vortex lines in two-dimensional Gross—Pitaevskii theory

Using the -mapping topological theory, we study the topological structure of vortex lines in a two-dimensional generalized Gross-Pitaevskii theory in (3+1)-dimensional space-time. We obtain the reduced dynamic equation in the framework of the two-dimensional Gross-Pitaevskii theory, from which a conserved dynamic quantity is derived on the stable vortex lines. Such equations can also be used to discuss Bose-Einstein condensates in heterogeneous and highly nonlinear systems. We obtain an exact dynamic equation with a topological term, which is ignored in traditional hydrodynamic equations. The explicit expression of vorticity as a function of the order parameter is derived, where the δ function indicates that the vortices can only be generated from the zero points of Φ and are quantized in terms of the Hopf indices and Brouwer degrees. The -mapping topological current theory also provides a reasonable way to study the bifurcation theory of vortex lines in the two-dimensional Gross-Pitaevskii theory.     

Gravitational Effects on the Vortex Distribution in Relativistic Superfluid Stars

Neutron stars are supposed to be mainly formed by a neutron superfluid. The angular momentum is given by the vortex array within the fluid, and a good account of the observable effects is determined by its coupling with the crust. In this article we show that the gravitational field introduces important modifications in the vortex distribution and shape. The inertial frame dragging on the quantum fluid produces a decrease in the vortex density, which for realistic models is in the order of 15%. This effect is relevant for neutron star rotation models and can provide a good framework for checking the quantum effect of the frame dragging.     

Kelvin-wave cascade and decay of superfluid turbulence

Kelvin waves (kelvons), the distortion waves on vortex lines, play a key part in the relaxation of superfluid turbulence at low temperatures. We present a weak-turbulence theory of kelvons. We show that nontrivial kinetics arises only beyond the local-induction approximation and is governed by three-kelvon collisions; a corresponding kinetic equation is derived. We prove the existence of Kolmogorov cascade and find its spectrum. The qualitative analysis is corroborated by numeric study of the kinetic equation. The application of the results to the theory of superfluid turbulence is discussed.     

Topological textures and their bifurcation processes in 2D ferromagnetic thin films

In this paper, by the use of the topological current theory, the topological structures and the dynamic processes in thin-film ferromagnetic systems are investigated directly from the viewpoint of topology. It is found that the topological charge of a thin-film ferromagnetic system can be changed by annihilation or creation processes of opposite polarized vortex–antivortex pairs taking place at space–time singularities of the normalized magnetization vector field of the system, the variation of the topological charge is integer and can further be expressed in terms of the Hopf indices and Brouwer degrees of the magnetization vector field around the singularities. Moreover, the change of the topological charge of the system is crucial to vortex core reversal processes in ferromagnetic thin films. With the help of the topological current theory and implicit function theorem, the processes of vortex merging, splitting as well as vortex core reversal are discussed in detail.     

Introduction to the vortex sheet of superfluid He-A

It is well known that superfluids respond to rotation by forming vortex lines. It has been recently discovered that a different type of state consisting of a vortex sheet, instead of lines, can be created in the A phase of superfluid ³He. This paper presents an introduction to the vortex sheet. We first discuss ⁴He, where a vortex sheet is unstable. The way to realize a stable sheet in ³He-A is called a vortex soliton. It consists of a topologically stable domain wall to which nonsingular vorticity is bound. The vortex soliton has been observed by nuclear magnetic resonance, and its most prominent experimental properties are explained. The macroscopic shape of the sheet and the superfluid flow in a rotating container are discussed.     

Transitions from vortex lines to sheets: interplay of topology and dynamics in an anisotropic superfluid

In isotropic macroscopic quantum systems vortex lines can be formed while in anisotropic systems also vortex sheets are possible. Based on measurements of superfluid 3He-A, we present the principles which select between these two competing forms of quantized vorticity: sheets displace lines if the frequency of the external drive exceeds a critical limit. The resulting topologically stable state consists of multiple vortex sheets and has much faster dynamics than the state with vortex lines.     

Bell's inequality and universal quantum gates in a cold-atom chiral fermionic p-wave superfluid

We propose and analyze a probabilistic scheme to entangle two spatially separated topological qubits in a p{x}+ip{y} superfluid using controlled collisions between atoms in movable dipole traps and unpaired atoms inside vortex cores in the superfluid. We discuss how to test the violation of Bell's inequality with the generated entanglement. A set of universal quantum gates is shown to be implementable deterministically using the entanglement despite the fact that the entangled states can be created only probabilistically.     

Mutual friction in the laminar flow of superfluid helium II through capillary tubes

The Hall-Vinen-Bekarevich-Khalatnikov theory is applied to the laminar flow of superfluid helium through capillary tubes. Velocity profiles obtained for the superfluid are interpreted in terms of the motion of vortex rings. The thermodynamic potential gradient as a function of the average superfluid and normal fluid velocities compares favourably with recent experimental results. It is concluded that the vortex rings originate at the wall and disappear at the tube axis.     

Topological Excitation in Skyrme Theory

Based on the C-mapping topological current theory and the decomposition of gauge potential theory, we investigate knotted vortex lines and monopoles in Skyrme theory and simply discuss the branch processes （splitting, merging, and intersection） during the evolution of the monopoles.