Zitterbewegung in the honeycomb photonic lattice

The propagation of a wave packet in a honeycomb photonic lattice has been studied using the time-dependent wave packet dynamics. It is found that the wave packet, superposed from the positive and negative energy modes at the vicinity of the two inequivalent Dirac points, can transform into a double-ring structure, which is caused by the interference between the two positive and negative energy modes around the Dirac points and is closely related to the Zitterbewegung (ZB). Also, a possible way to detect the ZB effect is proposed in the honeycomb photonic lattice.     

Frontispiece: Photonic Floquet topological insulators in atomic ensembles

The feasibility of realizing a photonic Floquet topological insulator (PFTI) in an atomic ensemble is demonstrated by Yiqi Zhang et al. (pp. 331–338) . The interference of three coupling fields will split energy levels periodically, to form a periodic refractive index structure with honeycomb profile that can be adjusted by different frequency detunings and intensities of the coupling fields. This in turn will affect the appearance of Dirac cones in momentum space. When the honeycomb lattice sites are helically ordered along the propagation direction, gaps open at Dirac points, and one obtains a PFTI in an atomic vapor. An obliquely incident beam will be able to move along the zigzag edge of the lattice without scattering energy into the PFTI, due to the confinement of edge states. The appearance of Dirac cones and the formation of a photonic Floquet topological insulator can be shut down by the third‐order nonlinear susceptibility and opened up by the fifth‐order one.     

三光束激光干涉光刻的实现方法

分析了多光束空间分布产生的误差对图形的影响,通过计算优化得到三光束产生的干涉图形在整个面内有着更好的图形稳定性。利用氦镉激光光源通过特定的光学系统形成空间分布近似旋转对称的三束光, 对光致抗蚀剂进行干涉曝光,制作出了周期600 nm、高度350 nm的蜂窝状点阵,测量结果表明该系统具有很好的图形重复性和稳定性,同时降低了对于光学光路的精密性要求。     

The wavefunction of an anyon

We consider a two-dimensional spin system in a honeycomb lattice configuration that exhibits anyonic and fermionic excitations [Kitaev, cond-mat/0506438]. The exact spectrum that corresponds to the translationally invariant case of a vortex-lattice is derived from which the energy of a single pair of vortices can be estimated. The anyonic properties of the vortices are demonstrated and their generation and transportation manipulations are explicitly given. A simple interference experiment with six spins is proposed that can reveal the anyonic statistics of this model.     

Dimers Belonging to Three Orientations on Plane Honeycomb Lattices

It is well known that there are three types of dimers belonging to the three different orientations in a honeycomb lattice, and in each type all dimers are mutually parallel. Based on a previous result, we can compute the partition function of the dimer problem of the plane (free boundary) honeycomb lattices with three different activities by using the number of its pure dimer coverings (perfect matchings). The explicit expression of the partition function and free energy per dimer for many types of plane honeycomb lattices with fixed shape of boundaries is obtained in this way (for a shape of plane honeycomb lattices, the procedure that the size goes to infinite, corresponds to a way that the honeycomb lattice goes to infinite). From these results, an interesting phenomena is observed. In the case of the regions of the plane honeycomb lattice has zero entropy per dimer—when its size goes to infinite—though in the thermodynamic limit, there is no freedom in placing a dimer at all, but if we distinguish three types of dimers with nonzero activities, then its free energy per dimer is nonzero. Furthermore, a sufficient condition for the plane honeycomb lattice with zero entropy per dimer (when the three activities are equal to 1) is obtained. Finally, the difference between the plane honeycomb lattices and the plane quadratic lattices is discussed and a related problem is proposed.     

蓝紫光氮化镓光子晶体面射型激光器

设计、制作了蓝紫光氮化镓光子晶体面射型激光器结构,并测量其光学性质,探讨了光子晶体的晶格常数、边界形状及晶格种类对激光器特性的影响。激光器结构采用有机金属化学气相沉积法配合电子束光刻及感应耦合等离子体干蚀刻等技术制作。由角度解析光致发光系统测得绕射图案、激光发射光谱及发散角等光学性质。同时,使用平面波展开法及多重散射法计算光子晶体的能带结构与阈值增益。由实验结果得出,可由改变光子晶体的晶格常数达到调变激光器操作模态的目的。此外,光子晶体的边界形状对激光器波长及半高宽并无显著的影响,但圆形边界的阈值激发能量密度比六角形边界低0.3 mJ/cm²。另一方面,将六角晶格、四角晶格与蜂巢晶格的晶格种类进行比较,蜂巢晶格具有较小的激发能量密度（1.6 mJ/cm²）及发散角（1.3°）,而四角晶格的激发能量密度（3.8 mJ/cm²）及发散角（2.2°）为三者之中最大。多重散射法求得的阈值增益与实验结果相吻合,可视为快速有效设计光子晶体激光器结构的工具。本文研究成果对今后发展高功率蓝紫光氮化镓光子晶体面射型激光器具有指导意义。     

Unveiling the Link Between Fractional Schrödinger Equation and Light Propagation in Honeycomb Lattice

We suggest a real physical system — the honeycomb lattice — as a possible realization of the fractional Schrödinger equation (FSE) system, through utilization of the Dirac‐Weyl equation (DWE). The fractional Laplacian in FSE causes modulation of the dispersion relation of the system, which becomes linear in the limiting case. In the honeycomb lattice, the dispersion relation is already linear around the Dirac point, suggesting a possible connection with the FSE, since both models can be reduced to the one described by the DWE. Thus, we propagate Gaussian beams in three ways: according to FSE, honeycomb lattice around the Dirac point, and DWE, to discover universal behavior — the conical diffraction. However, if an additional potential is brought into the system, the similarity in behavior is broken, because the added potential serves as a perturbation that breaks the translational periodicity of honeycomb lattice and destroys Dirac cones in the dispersion relation.     

Photonic Floquet topological insulators in atomic ensembles

The feasibility of realizing a photonic Floquet topological insulator (PFTI) in an atomic ensemble is demonstrated. The interference of three coupling fields will split energy levels periodically, to form a periodic refractive index structure with honeycomb profile that can be adjusted by different frequency detunings and intensities of the coupling fields. This in turn will affect the appearance of Dirac cones in momentum space. When the honeycomb lattice sites are helically ordered along the propagation direction, gaps open at Dirac points, and one obtains a PFTI in an atomic vapor. An obliquely incident beam will be able to move along the zigzag edge of the lattice without scattering energy into the PFTI, due to the confinement of edge states. The appearance of Dirac cones and the formation of a photonic Floquet topological insulator can be shut down by the third‐order nonlinear susceptibility and opened up by the fifth‐order one.

     

Transport properties in the photonic super‐honeycomb lattice — a hybrid fermionic and bosonic system

We report on the transport properties of the super‐honeycomb lattice, the band structure of which possesses a flat band and Dirac cones, according to the tight‐binding approximation. The super‐honeycomb model combines the honeycomb lattice and the Lieb lattice and displays the properties of both. It also represents a hybrid fermionic and bosonic system, which is rarely seen in nature. By choosing the phases of input beams properly, the flat‐band mode of the super‐honeycomb lattice will be excited and the input beams will exhibit strong localization during propagation. On the other hand, if the modes of Dirac cones of the super‐honeycomb lattice are excited, one will observe conical diffraction. Furthermore, if the input beam is properly chosen to excite a sublattice of the super‐honeycomb lattice and the modes of Dirac cones with different pseudospins, e.g., by the three‐beam interference pattern, the pseudospin‐mediated vortices will be observed.

     

改进型蜂巢晶格结构光子晶体光纤的色散与非线性特性

结合蜂巢晶格与不同空气孔直径晶格二者的优势,提出一种改进犁蜂巢晶格结构光子晶体光纤,采用矢量光束传输法对该光纤的色散与非线性特性进行了数值模拟,分析了色散、非线性系数与其晶格参量之间的关系.数值结果表明,该光纤在1.2～1.6 μm波段内可以实现大负色散、色散平坦、正色散等多种色散特性;此外,晶格结构中空气孔直径的减小...     

Anomalous reduction of the β-decay rate due to resonant energy absorption

The solvable model of a periodic array of quantum dots in a magnetic field is investigated. It is shown that in the case of square lattice and irrational flux the energy spectrum of a charged particle in the array has a fractal structure. In the case of honeycomb lattice the existence of an additional splitting of magnetic bands related with lattice geometry. The position of the Van Hove singularities is determined.     

Unconventional Energy Bands and Chirality of Ultracold Atoms in Trilayer Honeycomb Lattice

We investigate ultracold fermionic atoms in the trilayer honeycomb lattice. In the low energy approximation, we derive an effective Hamiltonian for pseudospins. The energy spectrum shows a cubic form of the wavevector and is gapless. The quasiparticles and quasiholes are ehiral and show Berry＇s phase π when the wavevector adiabatically evolves along a closed circle, Furthermore, the experimental detection of the energy spectrum is proposed with Bragg scattering techniques.     

Magnon spin Nernst effect on the antiferromagnetic checkerboard lattice

In this paper we study topological effects in an anisotropic checkerboard antiferromagnetic lattice in the presence of the Dzyaloshinskii-Moriya interaction (DMI). The time reversal symmetry is broken by anisotropies in the Hamiltonian. However, in contrast to the honeycomb lattice, the DMI does not open a gap here. We calculate the energy spectrum of the magnons and the spin Nernst coefficient in the presence of a longitudinal temperature gradient.     

Effects of selective dilution on phase diagram and ground-state magnetizations of an Ising antiferromagnet on triangular and honeycomb lattices

We employ an effective-field theory with correlations in order to study the phase diagram and ground-state magnetizations of a selectively diluted Ising antiferromagnet on triangular and honeycomb lattices. Dilution of different sublattices with generally unequal probabilities results in a rather intricate phase diagram in the sublattice dilution parameters space. In the case of the frustrated triangular lattice antiferromagnet the selective dilution affects the degree of frustration which can lead to some peculiar phenomena, such as reentrant behavior of long-range order or unsaturated sublattice magnetizations at zero temperature. The selectively diluted Ising antiferromagnet on the honeycomb lattice is obtained as a special case when one sublattice of the triangular lattice is completely removed by dilution.     

Orbital order in Mott insulators of spinless p-band fermions

A gas of strongly interacting single-species (spinless) p-orbital fermionic atoms in 2D optical lattices is proposed and studied. Several interesting new features are found. In the Mott limit on a square lattice, the gas is found to be described effectively by an orbital exchange Hamiltonian equivalent to a pseudospin-1/2 XXZ model. For a triangular, honeycomb, or kagome lattice, the orbital exchange is geometrically frustrated and described by a new quantum 120 degrees model. We determine the orbital ordering on the kagome lattice, and show how orbital wave fluctuations select ground states via the order by disorder mechanism for the honeycomb lattice. We discuss experimental signatures of various orbital ordering.     

Half-filled Kondo lattice on the honeycomb lattice

The unique linear density of state around the Dirac points for the honeycomb lattice brings much novel features in strongly correlated models. Here we study the ground-state phase diagram of the Kondo lattice model on the honeycomb lattice at half-filling by using an extended mean-field theory. By treating magnetic interaction and Kondo screening on an equal footing, it is found that besides a trivial discontinuous first-order quantum phase transition between well-defined Kondo insulator and antiferromagnetic insulating state, there can exist a wide coexistence region with both Kondo screening and antiferromagnetic orders in the intermediate coupling regime. In addition, the stability of Kondo insulator requires a minimum strength of the Kondo coupling. These features are attributed to the linear density of state, which are absent in the square lattice. Furthermore, fluctuation effect beyond the mean-field decoupling is analyzed and the corresponding antiferromagnetic spin-density-wave transition falls into the O(3) universal class. Comparatively, we also discuss the Kondo necklace and the Kane-Mele-Kondo (KMK) lattice models on the same lattice. Interestingly, it is found that the topological insulating state is unstable to the usual antiferromagnetic ordered states at half-filling for the KMK model. The present work may be helpful for further study on the interplay between conduction electrons and the densely localized spins on the honeycomb lattice.     

Unconventional Energy Bands and Chirality of Ultracold Atoms in Trilayer Honeycomb Lattice

We investigate ultracold fermionic atoms in the trilayer honeycomb lattice. In the low energy approximation, we derive an effective Hamiltonian for pseudospins. The energy spectrum shows a cubic form of the wavevector and is gapless. The quasiparticles and quasiholes are chiral and show Berry's phase π when thewavevector adiabatically evolves along a closed circle. Furthermore, the experimental detection of the energy spectrum is proposed with Bragg scattering techniques.     

Wave propagation in two-dimensional periodic lattices

Plane wave propagation in infinite two-dimensional periodic lattices is investigated using Floquet-Bloch principles. Frequency bandgaps and spatial filtering phenomena are examined in four representative planar lattice topologies: hexagonal honeycomb, Kagomé lattice, triangular honeycomb, and the square honeycomb. These topologies exhibit dramatic differences in their long-wavelength deformation properties. Long-wavelength asymptotes to the dispersion curves based on homogenization theory are in good agreement with the numerical results for each of the four lattices. The slenderness ratio of the constituent beams of the lattice (or relative density) has a significant influence on the band structure. The techniques developed in this work can be used to design lattices with a desired band structure. The observed spatial filtering effects due to anisotropy at high frequencies (short wavelengths) of wave propagation are consistent with the lattice symmetries.     

Bond and site diluted Ising-model systems: A unified treatment

A unified effective-field approximation scheme for both quenched bond- and site-diluted Ising magnets is presented. The method, which can systematically include correlation effects, is illustrated by applying to a honeycomb lattice. We also comment on the relation between the present method and that recently proposed by Boccara.     

Honeycomb discharge for diesel exhaust cleaning

Selectivity and energy efficiency of plasma chemical processes can be significantly improved if plasma is combined with a catalyst. The generation of stable discharge plasma inside the narrow capillaries of an automobile catalytic honeycomb is, however, quite difficult. This paper presents a novel method which utilizes the combination of packed-bed or barrier discharge connected in series with the honeycomb capillaries. By the application of DC voltage across the capillaries, streamers are extended from the packed-bed discharge into the capillaries. With this method, ionization can be made inside fine channels of honeycomb catalyst made of insulating materials. This discharge is designated as “honeycomb discharge”. Electrical and optical characteristics of the honeycomb discharge are measured.