One-dimensional Lattice Research Articles

Coexistence of non-Hermitian skin effect and extended states in one-dimensional nonreciprocal lattices

Coexistence of non-Hermitian skin effect and extended states in one-dimensional nonreciprocal lattices

Algebraic Hastatic Order in One-Dimensional Two-Channel Kondo Lattice.

The two-channel Kondo lattice likely hosts a rich array of phases, including hastatic order, a channel symmetry breaking heavy Fermi liquid. We revisit its one-dimensional phase diagram using density matrix renormalization group and, in contrast to previous work, find algebraic hastatic orders generically for stronger couplings. These are heavy Tomonaga-Luttinger liquids with nonanalyticities at Fermi vectors captured by hastatic density waves. We also find a predicted additional nonlocal order parameter due to interference between hastatic spinors, not present at large N, and residual repulsive interactions at strong coupling suggesting non-Fermi-liquid physics in higher dimensions.

Clock with 8×10^{-19} Systematic Uncertainty.

We report an optical lattice clock with a total systematic uncertainty of 8.1×10^{-19} in fractional frequency units, representing the lowest uncertainty of any clock to date. The clock relies on interrogating the ultranarrow ^{1}S_{0}→^{3}P_{0} transition in a dilute ensemble of fermionic strontium atoms trapped in a vertically-oriented, shallow, one-dimensional optical lattice. Using imaging spectroscopy, we previously demonstrated record high atomic coherence time and measurement precision enabled by precise control of collisional shifts and the lattice light shift. In this work, we revise the black body radiation shift correction by evaluating the 5s4d ^{3}D_{1} lifetime, necessitating precise characterization and control of many body effects in the 5s4d ^{3}D_{1} decay. Last, we measure the second order Zeeman coefficient on the least magnetically sensitive clock transition. All other systematic effects have uncertainties below 1×10^{-19}.

Interference-induced suppression of particle emission from a Bose–Einstein condensate in lattice with time-periodic modulations

Abstract Emission of matter-wave jets from a parametrically driven condensate has attracted significant experimental and theoretical attention due to the appealing visual effects and potential metrological applications. In this work, we investigate the collective particle emission from a Bose–Einstein condensate confined in a one-dimensional lattice with periodically modulated interparticle interactions. We give the regimes for discrete modes, and find that the emission can be distinctly suppressed. The configuration induces a broad band, but few particles are ejected due to the interference of the matter waves. We further qualitatively model the emission process and demonstrate the short-time behaviors. This engineering provides a way to manipulate the propagation of particles and the corresponding dynamics of condensates in lattices, and may find application in the dynamical excitation control of other nonequilibrium problems with time-periodic driving.

On The Thermalization of One-Dimensional Lattices. I. Microcanonical Ensemble

In numerical simulation of biomacromolecule, the issues of thermalization, i.e., equal distribution of energy over the degrees of freedom, occupy an important place. In this paper we consider some mechanisms of lattice thermalization: Chirikov resonances, wave turbulence and some others. We consider thermalization in a microcanonical ensemble when the system is isolated from external fields and the total energy is conserved. Although microcanonical ensembles are rarely used in practical calculations, however, the basic ideas about the thermalization mechanisms are obtained for these systems. The main attention is paid to the consideration of the lattices thermalization with Fermi-Pasta-Ulam-Tsingou potentials, since the main efforts to understand the basis of thermalization have been made precisely for lattices of this type. The role of solitons and breathers in thermalization is discussed.

High performance and compact antenna with new scheme for broadband circular polarisation applications

ABSTRACT In this research paper, the authors propose a unique broad-band circularly polarised antenna design with a sequentially rotated feed network intended for applications in the WiMAX IEEE 802.16, C-band, and ITU-R F386.9 bands. A sequential feeding approach utilising transmission lines with varying impedance properties and lengths has been utilised to properly stimulate the amplitude and phase distribution of each radiation element. To facilitate the rotation of the surface current distribution on the ground plane and further improve impedance matching, four L-shaped slits have been inserted into each corner of the ground plane along with a pair of mirrored slits of identical geometry within the antenna ground plane. The individual antenna element achieves an impedance bandwidth between 5–6.8 GHz and a 3 dB axial ratio bandwidth from 5.1–6.6 GHz. To additionally advance the radiation performance, the elements are configured into a 2 × 2 antenna and are interconnected utilising a sequentially rotated feeding network to attain broader axial ratio and impedance bandwidths. A key benefit of the implemented feed network is the minimisation of coupling effects between elements. To significantly increase the performance metrics of the antenna with limited increase to its physical size, electromagnetic band gap structures were incorporated as a one-dimensional lattice between the radiating elements. For the resulting antenna, an axial ratio bandwidth from 4.19 to 6.8 GHz (48%) and an impedance bandwidth spanning 2.9 to 9.8 GHz (102%) are achieved. The peak gain of the antenna is 11.2 dBic.

Complete photonic bandgap in a low-index two-dimensional quasicrystalline structure.

A bandgap in the continuum spectrum of photons in addition to its basic physical significance has strong potential for applications. Analogous to semiconductor crystals for electrons, periodic dielectric structures named photonic crystals were proposed to control photon flux propagation. In our search for low refractive index (RI) structures with a photonic bandgap, initial research efforts were focused on photonic crystal design, while aperiodic structures allow lower values of refractive index contrast to sustain a photonic bandgap. Here, we report on a two-dimensional quasicrystalline structure designed as a set of one-dimensional lattices merged into a single binary structure made of two materials with refractive index contrast 2|n1 - n2|/(n1 + n2) = 0.16 and even less in theory. We confirmed the theoretical prediction of bandgap exciting by measuring the radiation suppression of a dipole source placed in the center of the quasicrystalline structure. The full-wave numerical simulations and the experimental study appear to be in good agreement with the theoretical model.

Exact counterdiabatic driving in finite topological lattice models

Adiabatic protocols are often employed in state preparation schemes but require the system to be driven by a slowly varying Hamiltonian so that transitions between instantaneous eigenstates are exponentially suppressed. Counterdiabatic driving is a technique to speed up adiabatic protocols by including additional terms calculated from the instantaneous eigenstates that counter diabatic excitations. However, this approach requires knowledge of the full eigenspectrum meaning that the exact analytical form of counterdiabatic driving is only known for a subset of problems, e.g., the harmonic oscillator and transverse field Ising model. We extend this subset of problems to include the general family of one-dimensional noninteracting lattice models with open boundary conditions and arbitrary onsite potential, tunneling terms, and lattice size. We will derive a general analytical form for the counterdiabatic term for all states of lattice models, including bound and in-gap states which appear, e.g., in topological insulators. We also derive the general analytical form of targeted counterdiabatic driving terms which are tailored to enforce the dynamical state to remain in a specific state. As an example of the use of the derived analytical forms, we consider state transfer using the topological edge states of the Su-Schrieffer-Heeger model. The derived analytical counterdiabatic driving Hamiltonian can be utilized to inform control protocols in many-body lattice models or to probe the nonequilibrium properties of lattice models. Published by the American Physical Society 2024

Slow energy relaxation in anharmonic chains with and without on-site potentials: Roles of distinct types of discrete breathers

Slow energy relaxation has been observed in one-dimensional lattices with and without a nonlinear on-site potential; however, a comprehensive understanding of the detailed relaxation process remains elusive. Here we revisit this issue by introducing damping conditions at the free-end boundary of a thermalized lattice. We reveal that, in the long-cooling-time regime considered, for systems with a nonlinear on-site potential, energy relaxation exhibits a strong temperature-dependent behavior and with the increase of temperature, there is a crossover between decaying and non-decaying behaviors, around a crossover temperature point of Tc≃4.2. This non-decaying behavior at higher temperature is attributed to the presence of standing multi Sievers–Takeno discrete breather (DB) states. Conversely, for systems without on-site potentials, relaxation is nearly independent of temperature but dependent on interparticle potential. Notably, we observe that the cubic anharmonicity can generate moving single Page DB states that contribute to the unusual slow energy relaxation within a specific time regime. Our results provide enhanced insights into the mechanisms governing slow energy relaxation during lattice cooling.

Effective boundary conditions for second-order homogenization

Using matched asymptotic expansions, we derive an equivalent bar model for a periodic, one-dimensional lattice made up of linear elastic springs connecting both nearest and next-nearest neighbors. We obtain a strain-gradient model with effective boundary conditions accounting for the boundary layers forming at the endpoints. It is accurate to second order in the scale separation parameter ɛ≪1, as shown by a comparison with the solution to the discrete lattice problem. The homogenized modulus associated with the gradient effect (gradient stiffness) is found negative, as is often the case in second-order homogenization. Negative gradient stiffnesses are widely viewed as paradoxical as they can induce short-wavelength oscillations in the homogenized solution. In the one-dimensional lattice, the asymptotically correct boundary conditions are shown to suppress the oscillations, thereby restoring consistency. By contrast, most of the existing work on second-order homogenization makes use of postulated boundary conditions which, we argue, not only ruin the order of the approximation but are also the root cause of the undesirable oscillations.

Dynamical encircling of multiple exceptional points in anti-PT symmetry system

Exceptional points (EPs) in non-Hermitian systems have turned out to be at the origin of many intriguing effects with no counterparts in Hermitian cases. A typically interesting behavior is the chiral mode switching by dynamically winding the EP. Most encircling protocols focus on the two-state or parity-time (PT) symmetry systems. Here, we propose and investigate the dynamical encircling of multiple EPs in an anti-PT-symmetric system, which is constructed based on a one-dimensional lattice with staggered lossy modulation. We reveal that dynamically encircling the multiple EPs results in the chiral dynamics via multiple non-Hermiticity-induced nonadiabatic transitions, where the output state is always on the lowest-loss energy sheet. Compared with the PT-symmetric systems that require complicated variation of the gain/loss rate or on-site potentials, our system only requires modulations of the couplings which can be readily realized in various experimental platforms. Our scheme provides a route to study non-Hermitian physics by engineering the EPs and implement novel photonic devices with unconventional functions.

Quantum ratchet with Lindblad rate equations.

A quantum random-walk model is established on a one-dimensional periodic lattice that fluctuates between two possible states. This model is defined by Lindblad rate equationsthat incorporate the transition rates between the two lattice states. Leveraging the system's symmetries, the particle velocity can be described using a finite set of equations, even though the state space is of infinite dimension. These equationsyield an analytical expression for the velocity in the long-time limit, which is employed to analyze the characteristics of directed motion. Notably, the velocity can exhibit multiple inversions, and to achieve directed motion, distinct, nonzero transition rates between lattice states are required.

On the structure factor of jammed particle configurations on the one-dimensional lattice

A broad class of blocked or jammed configurations of particles on the one-dimensional lattice can be characterized in terms of local rules involving only the lengths of clusters of particles (occupied sites) and of holes (empty sites). Examples of physical relevance include the metastable states reached by the zero-temperature dynamics of kinetically constrained spin chains, the attractors of totally irreversible processes such as random sequential adsorption, and arrays of Rydberg atoms in the blockade regime. The configurational entropy of ensembles of such blocked configurations has been investigated recently by means of an approach inspired from the theory of stochastic renewal processes. This approach provides a valuable alternative to the more traditional transfer-matrix formalism. We show that the renewal approach is also an efficient tool to investigate a range of observables in uniform ensembles of blocked configurations, besides their configurational entropy. The main emphasis is on their structure factor and correlation function.

Finite-element assembly approach of optical quantum walk networks

We present a finite-element approach for computing the aggregate scattering matrix of a network of linear coherent scatterers. These might be optical scatterers or more general scattering coins studied in quantum walk theory. While techniques exist for two-dimensional lattices of feed-forward scatterers, the present approach is applicable to any network configuration of any collection of scatterers. Unlike traditional finite-element methods in optics, this method does not directly solve Maxwell’s equations; instead it is used to assemble and solve a linear, coupled scattering problem that emerges after Maxwell’s equations are abstracted within the scattering matrix method. With this approach, a global unitary is assembled corresponding to one time step of the quantum walk on the network. After applying the relevant boundary conditions to this global matrix, the problem becomes non-unitary and possesses a steady-state solution that is the output scattering state. We provide an algorithm to obtain this steady-state solution exactly using a matrix inversion, yielding the scattering state without requiring a direct calculation of the eigenspectrum. The approach is then numerically validated on a coupled-cavity interferometer example that possesses a known, closed-form solution. Finally, the method is shown to be a generalization of the Redheffer star product, which describes scatterers on one-dimensional lattices (2-regular graphs) and is often applied to the design of thin-film optics, making the current approach an invaluable tool for the design and validation of high-dimensional phase-reprogrammable optical devices and study of quantum walks on arbitrary graphs.

Non-abelian discrete Toda chains and related lattices

We have derived a non-abelian analog for the two-dimensional discrete Toda lattice which possesses solutions in terms of quasideterminants and admits Lax pairs of different forms. Its connection with non-abelian analogs for several well-known (1+1) and one-dimensional lattices is discussed. In particular, we consider a non-commutative analog of the scheme: discrete Toda equations → Somos-N sequences → discrete Painlevé equations.

Photonic random walks with traps.

Random walks (RW) behave very differently for classical and quantum particles. Here we unveil a ubiquitous distinctive behavior of random walks of a photon in a one-dimensional lattice in the presence of a finite number of traps, at which the photon can be destroyed and the walk terminates. While for a classical random walk, the photon is unavoidably destroyed by the traps. For a quantum walk, the photon can remain alive, and the walk continues forever. Such an intriguing behavior is illustrated by considering photonic random walks in synthetic mesh lattices with controllable decoherence, which enables the switch from quantum to classical random walks.

Introduction of Local Resonators to a Nonlinear Metamaterial With Topological Features

Abstract Recent work in nonlinear topological metamaterials has revealed many useful properties such as amplitude dependent localized vibration modes and nonreciprocal wave propagation. However, thus far, there have not been any studies to include the use of local resonators in these systems. This work seeks to fill that gap through investigating a nonlinear quasi-periodic metamaterial with periodic local resonator attachments. We model a one-dimensional metamaterial lattice as a spring-mass chain with coupled local resonators. Quasi-periodic modulation in the nonlinear connecting springs is utilized to achieve topological features. For comparison, a similar system without local resonators is also modeled. Both analytical and numerical methods are used to study this system. The dispersion relation of the infinite chain of the proposed system is determined analytically through the perturbation method of multiple scales. This analytical solution is compared to the finite chain response, estimated using the method of harmonic balance and solved numerically. The resulting band structures and mode shapes are used to study the effects of quasi-periodic parameters and excitation amplitude on the system behavior both with and without the presence of local resonators. Specifically, the impact of local resonators on topological features such as edge modes is established, demonstrating the appearance of a trivial bandgap and multiple localized edge states for both main cells and local resonators. These results highlight the interplay between local resonance and nonlinearity in a topological metamaterial demonstrating for the first time the presence of an amplitude invariant bandgap alongside amplitude dependent topological bandgaps.

Super-ballistic diffusion induced by nonlinear interactions in a one-dimensional quasiperiodic lattice

We numerically investigate the spreading dynamics of wave packets in a one-dimensional lattice with quasiperiodic disorders and nonlinear interactions. Under moderate disorder strength, we reveal an intriguing super-ballistic diffusion driven by increasing the interaction strength from the ballistic diffusion in the non- and weakly interacting cases. We obtain a wide parameter region for such a faster-than-ballistic spreading of wave packets in the quasiperiodic lattice, although the nonlinear self-trapping is dominated under strong interactions. The super-ballistic diffusion is further analyzed based on the point source model. We also show the interaction-induced sub-diffusive spreading in the Anderson localized regime. The super-ballistic and sub-diffusive dynamics are exhibited in the spreading that starts from both the single-site and Gaussian wave packets. Our results showcase the interaction-enabled super-ballistic diffusion, which is scarce and experimentally realizable in artificial atomic or photonic lattices.

Magnetic order and strongly correlated effects in the one-dimensional Ising-Kondo lattice

Magnetic order and strongly correlated effects in the one-dimensional Ising-Kondo lattice

Unidirectional photonic reflector using a defective atomic lattice

Based on the broken spatial symmetry, we propose a scheme for engineering a unidirectional photonic reflector using a one-dimensional atomic lattice with defective cells that have been specifically designed to be vacant. By trapping three-level atoms and driving them into the regime of electromagnetically induced transparency, and through the skillful design of the number and position of vacant cells in the lattice, numerical simulations demonstrate that a broad and high unidirectional reflection region can be realized within the EIT window. This proposed unidirectional reflector scheme provides a new platform for achieving optical nonreciprocity and has potential applications for designing optical circuits and devices of nonreciprocity at extremely low energy levels. Published by the American Physical Society 2024