Static Lattices Research Articles

All‐Bands‐Flat Floquet Topological Photonic Insulators with Microring Lattices

Coupled microring lattices are versatile photonic systems that can be used to realize various topological phases of matter. In two‐dimensional (2D) microring lattices, the periodic and unidirectional circulation of light in each microring gives rise to a time‐like dimension, so that the lattice emulates a (2 + 1)D system with much richer topological behaviors than static 2D lattices. Accurate treatment of these systems requires a departure from the static tight‐binding model of coupled resonators and take into account the periodic coupling sequence of light in the lattice network. This article provides an overview of the theory and design of (2 + 1)D microring lattices for realizing Floquet topological photonic insulators (TPIs). Particular focus is placed on the microring Lieb lattice with perfect couplings, which emulates an anomalous Floquet insulator with all flat bands. Such a system exhibits some unique properties, including wide edge mode continuum exceeding a Floquet–Brillouin zone, super‐robustness to lattice disorder, Aharonov–Bohm (AB) caging and compact localized flat‐band states that can be used to realize high‐quality factor topological resonators. All‐bands‐flat Floquet–Lieb microring lattices provide a versatile platform for investigating topological physics as well as potential applications in realizing topologically‐protected photonic devices.

Materials properties of defect-stabilized off-stoichiometric τ-phase Al2Ge2Mg

We have performed a quantum-mechanical study of off-stoichiometric Al2Ge2Mg τ-phase intermetallic compounds. Our calculations focused on evaluating the formation energy of static lattices, their elastic properties as well as free energy of formation including phonon contributions. While the stoichiometric Al2Ge2Mg τ phase was found thermodynamically, mechanically and dynamically stable, we have identified an off-stoichiometric composition Al7Ge8Mg5 which exhibits the free energy of formation lower than the stoichiometric compound. The Al7Ge8Mg5 was found both mechanically and dynamically stable as well. This off-stoichiometric compound has Mg atoms located also at the Al sublattice, i.e. these defects exhibit a stabilizing effect. Phonon contributions into the free energy of formation have turned out to be crucial for a proper description of the thermodynamic stability. In contrast, several other off-stoichiometric states are significantly thermodynamically destabilized by anti-site atoms at the Ge sublattice. The formation energy and the homogenized polycrystal Young's modulus are found anti-correlated indicating a connection between the thermodynamic and mechanical stability. Regarding the theoretical values of homogenized polycrystal Young's moduli, our measurements resulted in values quite close to the predicted ones.

Low thermal expansion of layered electrides predicted by density-functional theory.

Layered electrides are a unique class of materials with anionic electrons bound in interstitial regions between thin, positively charged atomic layers. While density-functional theory is the tool of choice for computational study of electrides, there has to date been no systematic comparison of density functionals or dispersion corrections for their accurate simulation. There has also been no research into the thermomechanical properties of layered electrides, with computational predictions considering only static lattices. In this work, we investigate the thermomechanical properties of five layered electrides using density-functional theory to evaluate the magnitude of thermal effects on their lattice constants and cell volumes. We also assess the accuracy of five popular dispersion corrections with both planewave and numerical atomic orbital calculations.

Supersolid gap soliton in a Bose-Einstein condensate and optical ring cavity coupling system.

The system of a transversely pumped Bose-Einstein condensate (BEC) coupled to a lossy ring cavity can favor a supersolid steady state. Here we find the existence of supersolid gap soliton in such a driven-dissipative system. By numerically solving the mean-field atom-cavity field coupling equations, gap solitons of a few different families have been identified. Their dynamical properties, including stability, propagation, and soliton collision, are also studied. Due to the feedback atom-intracavity field interaction, these supersolid gap solitons show numerous new features compared with the usual BEC gap solitons in static optical lattices.

Nonlinear signatures of Floquet band topology

We study how the nonlinear propagation dynamics of bulk states may be used to distinguish topological phases of slowly driven Floquet lattices. First, we show how instabilities of nonlinear Bloch waves may be used to populate Floquet bands and measure their Chern number via the emergence of nontrivial polarization textures in a similar manner to static (undriven) lattices. Second, we show how the nonlinear dynamics of nonstationary superposition states may be used to identify dynamical symmetry inversion points in the intracycle dynamics, thereby allowing anomalous Floquet phases to be distinguished from the trivial phase. The approaches may be readily implemented using light propagation in nonlinear waveguide arrays.

Isothermal calorimetry measurements of ion binding and DNA condensation as a function of DNA length

Despite decades of theoretical and experimental research, the mechanism of ion-driven DNA condensation remains elusive. Numerous models successfully describe this condensation, including those invoking dynamic counterion fluctuations, salt bridges, static counterion lattices, and models that invoke the underlying DNA geometry, all while presenting different models for ion binding, DNA self-attraction, and the underlying energy landscape. We present research on isothermal calorimetry (ITC) of DNA condensation to extract the thermodynamic parameters that drive this process.

Trapping light in a Floquet topological photonic insulator by Floquet defect mode resonance

Floquet topological photonic insulators characterized by periodically varying Hamiltonians are known to exhibit much richer topological behaviors than static systems. In a Floquet insulator, the phase evolution of the Floquet–Bloch modes plays a crucial role in determining its topological behaviors. Here, we show that by perturbing the driving sequence, it is possible to manipulate the cyclic phase change in the system over each evolution period to induce self-interference of a bulk mode, leading to a resonance effect, which can be regarded as a Floquet counterpart of defect-mode resonance in static lattices. This Floquet Defect Mode Resonance (FDMR) is cavity-less since it does not require physical boundaries; its spatial localization pattern is, instead, determined by the driving sequence and is found to be different in topologically trivial and nontrivial lattices. We demonstrated excitation of FDMRs by edge modes in a Floquet octagon lattice on silicon-on-insulator, achieving extrinsic quality factors greater than 104. Imaging of the scattered light pattern directly revealed the hopping sequence of the Floquet system and confirmed the spatial localization of FDMR in a bulk-mode loop. The new Floquet topological resonator could find various applications in lasers, optical filters and switches, nonlinear cavity optics, and quantum optics.

The Impact of Vibrational Entropy on the Segregation of Cu to Antiphase Boundaries in Fe3Al

We performed a quantum mechanical study of segregation of Cu atoms toward antiphase boundaries (APBs) in Fe3Al. The computed concentration of Cu atoms was 3.125 at %. The APBs have been characterized by a shift of the lattice along the ⟨001⟩ crystallographic direction. The APB energy turns out to be lower for Cu atoms located directly at the APB interfaces and we found that it is equal to 84 mJ/m2. Both Cu atoms (as point defects) and APBs (as extended defects) have their specific impact on local magnetic moments of Fe atoms (mostly reduction of the magnitude). Their combined impact was found to be not just a simple sum of the effects of each of the defect types. The Cu atoms are predicted to segregate toward the studied APBs, but the related energy gain is very small and amounts to only 4 meV per Cu atom. We have also performed phonon calculations and found all studied states with different atomic configurations mechanically stable without any soft phonon modes. The band gap in phonon frequencies of Fe3Al is barely affected by Cu substituents but reduced by APBs. The phonon contributions to segregation-related energy changes are significant, ranging from a decrease by 16% at T = 0 K to an increase by 17% at T = 400 K (changes with respect to the segregation-related energy difference between static lattices). Importantly, we have also examined the differences in the phonon entropy and phonon energy induced by the Cu segregation and showed their strongly nonlinear trends.

Long Josephson junctions with exciton-polariton condensates

We demonstrate the possibility to build stable Josephson $\pi$-junction stripes with exciton-polariton condensates. The stability of the $\pi$-junction between arbitrary long polariton stripes is achieved at low pumping by balancing the snaking instability with counter-propagating flows towards the junction. Not dissimilar from a dark soliton, the instability becomes relevant at high pumping leading to formation of vortex dipoles. The resulting structures can be stabilised to produce static lattices of Josephson vortices in straight and ring geometries. Our results build towards realization of quantum technological applications based on the Josephson effect at room temperature.

Lattice-Modeled Information Flow Control of Big Sensing Data Streams for Smart Health Application

Internet of Things (IoT) provides a promising opportunity to build powerful data analytics systems with real time event detection for smart health, and therefore wearable IoT has become a rising source of big data streams for smart health, for which security needs to be assured by detecting real-time event to avoid malicious activities, and meanwhile to control the information leakage of big sensing data streams. I refer to this as an information flow control problem. To address this problem, this paper proposes a static lattice model for information flow control over big sensing data streams. I initialize two static lattices, i.e., sensor lattice for wearable sensors and user lattice for users, and then static lattices aim to process the flow control model faster, because I am dealing with high volume and velocity of data streams. The experimental evaluation and results of the information flow model show that it can excellently handle the incoming big data streams with low latency and buffer requirement.

Ion Binding and Electrostatics in Condensed DNA Arrays Probed by Ion Counting Techniques

Despite decades of theoretical and experimental research, the mechanism of DNA condensation remains elusive. Numerous models successfully describe this condendsation, including those invoking dynamic counterion fluctuations, salt bridges, static counterion lattices, and models that invoke the underlying DNA geometry, all while presenting vastly different models for ion binding. Here we present new experimental data that quantifies the ions bound to condensed DNA arrays. By measuring the competition between condensing ions and various non-condensing ions we quantify the electrostatic interactions between the DNA and ions. Furthermore, by varying the inter-axial spacing of condensed DNA utilizing crowding agents, we report on the interplay between the packing force of DNA and competitive ion binding. Finally, we present a simple new Ion Binding Model (IBM) that captures much of the observed binding. These data should prove vital in determining the underlying electrostatic mechanisms that drive DNA condensation.

On lattice sums and Wigner limits

Wigner limits are given formally as the difference between a lattice sum, associated to a positive definite quadratic form, and a corresponding multiple integral. To define these limits, which arose in work of Wigner on the energy of static electron lattices, in a mathematically rigorous way one commonly truncates the lattice sum and the corresponding integral and takes the limit along expanding hypercubes or other regular geometric shapes. We generalize the known mathematically rigorous two- and three-dimensional results regarding Wigner limits, as laid down in [3], to integer lattices of arbitrary dimension. In doing so, we also resolve a problem posed in [6, Chapter 7]. For the sake of clarity, we begin by considering the simpler case of cubic lattice sums first, before treating the case of arbitrary quadratic forms. We also consider limits taken along expanding hyperballs with respect to general norms, and connect with classical topics such as Gauss's circle problem. Appendix A is included to recall certain properties of Epstein zeta functions that are either used in the paper or serve to provide perspective.

Structure of electromagnetic fields near the surface of an ionic crystal

A NaCl ionic crystal whose (100) face is in contact with vacuum is used as an example to consider static and dynamic contributions to an electromagnetic field in close proximity to its surface. The expression for the potential of the electric field produced by a system of point charges in vacuum (derived by Lennard-Jones and Dent) is taken as the basis. The dynamic correction to the static field has been found. It appears as a result of thermal fluctuations of ions near equilibrium positions in the ionic lattice. Various contributions of the electrostatic field of the ionic lattice, the field of fluctuating ions of this lattice near their equilibrium positions, and of the dipole-type fluctuation field produced by spontaneous deformations of the crystal’s elementary cells to the energy density of the electromagnetic field near the surface of the ionic crystal have been calculated and compared. The periodic structuring of the electromagnetic field’s energy density caused by the presence of static and dynamic ionic lattices of the crystal at small distances from its surface is illustrated graphically. Fields generated by a film with a finite thickness containing an arbitrary number of ion monolayers have also been considered.

Diffusion of particles over dynamically disordered lattice

Using kinetic Monte Carlo simulations we have investigated the diffusion of particles over a lattice with moving atoms in the framework of a simple lattice-gas model of a reconstructive surface. The particle migration over the static and dynamic lattices differs considerably. The dynamic lattice reconstruction changes substantially the particle diffusion coefficient. The Arrhenius dependencies are quantitatively different. An interesting peculiarity of the particle migration is the formation of defectons--local lattice deformations around the adsorbed particles. In certain ranges of the system parameters (jump rates of the substrate atoms and adsorbed particles) the adsorbed particles cause local displacements of the nearest substrate atoms, resulting in deeper adsorption sites and lower jump rates. Such particle self-trapping produces a characteristic minimum on the Arrhenius dependencies.

Bidirectional transport on a dynamic lattice

Bidirectional variants of stochastic many particle models for transport by molecular motors show a strong tendency to form macroscopic clusters on static lattices. Inspired by the fact that the microscopic tracks for molecular motors are dynamical, we study the influence of different types of lattice dynamics on stochastic bidirectional transport. We observe a transition toward efficient transport (corresponding to the dissolution of large clusters) controlled by the lattice dynamics.

DNA Constraints Allow Rational Control of Macromolecular Conformation

We report that double-helical DNA constraints can be used to control the conformation of another molecule, RNA. When a covalently attached DNA constraint is structurally incompatible with the native Mg2+-dependent RNA conformation, RNA folding is disrupted, as revealed by nondenaturing gel electrophoresis and independently by chemical probing. Our approach is distinct from other efforts in DNA nanotechnology, which have prepared DNA objects by self-assembly, built static DNA lattices for assembly of other objects, and created nanomachines made solely of DNA. In contrast, our dynamic use of DNA to control the conformations of other macromolecules should have wide impact in nanotechnology applications ranging from materials science to biology.

Generation and application of femtosecond X-ray pulse

Generation and application of femtosecond X-ray pulses using the linac-laser synchronization system at Nuclear Engineering Research Laboratory, University of Tokyo, were performed. The time resolution of the synchronization between 240 fs (FWHM) 17 MeV electron pulse and 100 fs (FWHM) 3 TW Ti:Sapphire laser pulse is 3.5 ps (rms). Femtosecond X-ray pulses were generated via orthogonal and head-on Thomson scatterings between the electron and laser pulses. Then, the time-resolved X-ray diffraction was tried to visualize atomic motion in nonequilibrium thermal expansion in several mono-crystals. Here we generated picosecond X-ray pulse by colliding 10 ps electron pulse to 100 μm∅ Cu wire for simplicity. X-ray diffraction patterns of Cu K α 1,2 from the static lattices were obtained. Visualization of the atomic motion is under way.

Peculiarities of Energy Exchange Among Four Light Waves Spreading Forward in Media with Diagonal-Bipolar Response: Eigenmodes, Spatial Instability and Optical Switching

Interaction of four light waves in a nematic liquid crystal is studied theoretically. We graphically on the phase plane solve equations describing four wave mixing (FWM) under excitation of the static lattices of the dielectric permeability in the nematic liquid crystal. We show existence of unstable eigenmode in FWM. Effect of optical switching of energy is predicted. Energy exchange among the light waves depends on relative initial phase among the four waves. Experimental conditions, under which the effects that are studied would be observable, are discussed.

The Ising transition in 2D simplicial quantum gravity — can Regge calculus be right?

We report a high statistics simulation of Ising spins coupled to 2D quantum gravity in the Regge calculus approach using triangulated tori with up to 512 2 vertices. For the constant area ensemble and the dl / l functional measure we definitively can exclude the critical exponents of the Ising phase transition as predicted for dynamically triangulated surfaces. We rather find clear evidence that the critical exponents agree with the Onsager values for static regular lattices, independent of the coupling strength of an R 2 interaction term. For exploratory simulations using the lattice version of the Misner measure the situation is less clear.

First-principles calculation of the elastic stiffness tensor of aluminium nitride under high pressure

The first-principles method for calculating the elastic stiffness tensor of composite crystals has been given. Applying the present method to the wurtzite and rocksalt structures of AlN under normal and elevated pressure up to 25.8 GPa, we have determined the elastic stiffness tensor completely from first principles. The theoretical values for the wurtzite structure at normal pressure are in good agreement with the experimental ones given by Tsubouchi and Mikoshiba. The elastic stiffness constants have been evaluated from the total energies of the deformed static lattices. These energies have been calculated by using a calculation method based on the variational principle.