Lattice Potential Research Articles

Topological Floquet engineering of a three-band optical lattice with dual-mode resonant driving

We present a Floquet framework for controlling topological features of a one-dimensional optical lattice system with dual-mode resonant driving, in which both the amplitude and phase of the lattice potential are modulated simultaneously. We investigate a three-band model consisting of the three lowest orbitals and elucidate the formation of a crosslinked two-leg ladder through an indirect interband coupling via an off-resonant band. We numerically demonstrate the emergence of topologically nontrivial bands within the driven system, and a topological charge pumping phenomenon with cyclic parameter changes in the dual-mode resonant driving. Finally, we show that the band topology in the driven three-band system is protected by parity-time reversal symmetry. Published by the American Physical Society 2024

Particle-Hole Asymmetric Ferromagnetism and Spin Textures in the Triangular Hubbard-Hofstadter Model

In a lattice model subject to a perpendicular magnetic field, when the lattice constant is comparable to the magnetic length, one enters the “Hofstadter regime,” where continuum Landau levels become fractal magnetic Bloch bands. Strong mixing between bands alters the nature of the resulting quantum phases compared to the continuum limit; lattice potential, magnetic field, and Coulomb interaction must be treated on equal footing. Using determinant quantum Monte Carlo and density matrix renormalization group techniques, we study this regime numerically in the context of the Hubbard-Hofstadter model on a triangular lattice. In the field-filling phase diagram, we find a broad wedge-shaped region of ferromagnetic ground states for filling factor ν≤1, bounded below by filling factor ν=1 and bounded above by half filling the lowest Hofstadter subband. We observe signatures of SU(2) quantum Hall ferromagnetism at filling factors ν=1 and ν=3. The phases near ν=1 are particle-hole asymmetric, and we observe a rapid decrease in ground-state spin polarization consistent with the formation of skyrmions only on the electron doped side. At large fields, above the ferromagnetic wedge, we observe a low-spin metallic region with spin correlations peaked at small momenta. We argue that the phenomenology of this region likely results from exchange interaction mixing fractal Hofstadter subbands. The phase diagram derived beyond the continuum limit points to a rich landscape to explore interaction effects in magnetic Bloch bands. Published by the American Physical Society 2024

Fluid-filled lattices for responsive orthotic insoles

Abstract Orthotic insoles are essential for alleviating discomfort and preventing injuries in the foot caused by high peak pressures in the plantar tissue. Traditional orthotic insoles, often prescribed to address these issues, are designed based on the static foot shape and pressure measurements, lacking responsiveness to dynamic movements. This study explores the behaviour of fluid-filled lattices for improving the functionality of orthotic insoles, focusing on energy dissipation and pressure redistribution capabilities. Using numerical homogenisation, the research integrates hyperelastic and permeability models to simulate the behaviour of Solid–Liquid Composites. Experimental tests validated these models, examining the influence of fluid viscosity and structural variations on energy dissipation and pressure distribution. Results show that fluid-filled lattices provide enhanced energy dissipation and reduce peak pressures by evening out the pressure distribution compared to non-fluid-filled samples. These findings highlight the potential of fluid-filled lattices to improve the performance and comfort of orthotic insoles.

High Mechanical Performance of Lattice Structures Fabricated by Additive Manufacturing

Lattice structures show advantages in mechanical properties and energy absorption efficiency owing to their lightweight, high strength and adjustable geometry. This article reviews lattice structure classification, design and applications, especially those based on additive manufacturing (AM) technology. This article first introduces the basic concepts and classification of lattice structures, including the classification based on topological shapes, such as strut, surface, shell, hollow-strut, and so on, and the classification based on the deformation mechanism. Then, the design methods of lattice structure are analyzed in detail, including the design based on basic unit, mathematical algorithm and gradient structure. Next, the effects of different lattice elements, relative density, material system, load direction and fabrication methods on the mechanical performance of AM-produced lattice structures are discussed. Finally, the advantages of lattice structures in energy absorption performance are summarized, aiming at providing theoretical guidance for further optimizing and expanding the engineering application potential of lattices.

Symmetry and Value of the Order Parameter in 2d Nematic Superconductors

We derive equations for the superconducting nematic order parameter and chemical potential for the hexagonal lattice by accounting for nearest- and next-nearest-neighbor hoppings of electrons. By analyzing the energy of the superconducting ground state, we have found that the symmetry of the order parameter and some other superconducting properties of the system strongly depend on the sign and the magnitude of the next-nearest neighbor hopping. As we will demonstrate, both extended s- and d-pairings significantly contribute to the pairing in the system, that be tuned by changing the hopping parameters. We discuss a possible connection of the obtained results to the properties of several doped monolayer superconductors – graphene and transition metal dichalcogenides.

Anticipating Pressure Changes in Halides under Compression

A new equation of state (NEOS) for Halides has been developed using the theory of lattice potential and the concept of volume dependence of the short-range force constant. The derivation of this equation of state involved the use of the third-order approximation of the lattice potential. A comparative analysis was conducted between the isothermal equations of state, including Vinet EOS, Murnaghan EOS, Holzapfel EOS, Born-Mie EOS, Birch-Murnaghan EOS, and the newly derived NEOS. The NEOS was used to analyze the compression behavior of Halides, and it was found that Vinet EOS and NEOS agreed with the experimental data for Halides up to high compression. However, Murnaghan EOS, Born-Mie EOS, Holzapfel EOS, and Birch-Murnaghan EOS are usually less sensitive to calculating pressure at high compression. It was also observed that for some Halides, such as NaBr and NaI, Vinet EOS could not produce results consistent with experimental findings. In contrast, NEOS consistently produced results that matched the experimental findings for all Halides samples, unequivocally demonstrating its reliability and accuracy.

Effect of unit cell rotation on mechanical performance of selective laser melted Gyroid structures for bone tissue engineering

Gyroid lattice structures, inspired by the natural interconnectivity of human bone, show promise in bone tissue engineering (BTE). This study explores the mechanical properties, and failure mechanisms of selective laser melted (SLM) Gyroid Ti6Al4V lattice structures with varying unit cell rotation angles (RA) of 0∘ (G0), 30∘ (G30), and 60∘ (G60) around the x-axis. The study assesses their mechanical and energy absorption properties through quasi-static compression testing and elastoplastic finite element (FE) analysis. Despite similar relative densities for all designed lattices, the RA variation significantly impacts mechanical performance. G30 exhibits superior load-bearing capacity, with higher modulus of elasticity, yield strength, ultimate strength, and plateau stress. It also has the highest energy absorption capacity, while G60 shows the highest surface area (SA) and surface area-to-volume ratio (SA/VR). These findings highlight the potential of Gyroid lattices for bone replacements due to their tunable mechanical and biological responses.

Multidisciplinary design optimisation of lattice-based battery housing for electric vehicles

Batteries with high energy densities become essential with the increased uptake of electric vehicles. Battery housing, a protective casing encapsulating the battery, must fulfil competing engineering requirements of high stiffness and effective thermal management whilst being lightweight. In this study, a graded lattice design framework is developed based on topology optimisation to effectively tackle the multidisciplinary objectives associated with battery housing. It leverages the triply periodic minimal surfaces lattices, aiming for high mechanical stiffness and efficient heat dissipation considering heat conduction and convection. The effectiveness of the proposed framework was demonstrated through the battery housing design, showcasing its ability to address multidisciplinary objectives as evidenced by the analysis of the Pareto front. This study identifies the potential of lattices in lightweight applications incorporating multiphysics and offers an efficient lattice design framework readily extended to other engineering challenges.

Codebase release r0.3 for SmoQyDQMC.jl

We introduce the SmoQyDQMC.jl package, a Julia implementation of the determinant quantum Monte Carlo algorithm. SmoQyDQMC.jl supports generalized tight-binding Hamiltonians with on-site Hubbard and generalized electron-phonon (ee-ph) interactions, including non-linear ee-ph coupling and anharmonic lattice potentials. Our implementation uses hybrid Monte Carlo methods with exact forces for sampling the phonon fields, enabling efficient simulation of low-energy phonon branches, including acoustic phonons. The SmoQyDQMC.jl package also uses a flexible scripting interface, allowing users to adapt it to different workflows and interface with other software packages in the Julia ecosystem. The code for this package can be downloaded from our GitHub repository at https://github.com/SmoQySuite/SmoQyDQMC.jl or installed using the Julia package manager. The online documentation, including examples, can be obtained from our document page at https://smoqysuite.github.io/SmoQyDQMC.jl/stable/.

SmoQyDQMC.jl: A flexible implementation of determinant quantum Monte Carlo for Hubbard and electron-phonon interactions

We introduce the SmoQyDQMC.jl package, a Julia implementation of the determinant quantum Monte Carlo algorithm. SmoQyDQMC.jl supports generalized tight-binding Hamiltonians with on-site Hubbard and generalized electron-phonon (ee-ph) interactions, including non-linear ee-ph coupling and anharmonic lattice potentials. Our implementation uses hybrid Monte Carlo methods with exact forces for sampling the phonon fields, enabling efficient simulation of low-energy phonon branches, including acoustic phonons. The SmoQyDQMC.jl package also uses a flexible scripting interface, allowing users to adapt it to different workflows and interface with other software packages in the Julia ecosystem. The code for this package can be downloaded from our GitHub repository at https://github.com/SmoQySuite/SmoQyDQMC.jl or installed using the Julia package manager. The online documentation, including examples, can be obtained from our document page at https://smoqysuite.github.io/SmoQyDQMC.jl/stable/.

Nonlinear Transport through Parity–Time Symmetric Lattice Potentials

We study nonlinear transports of a light field through finite parity–time symmetric lattice potentials. The initial light field is trapped in a source reservoir and is released to expand toward the lattice potentials along the transverse direction due to the nonlinearity. We identify the transports that can be classified into in-band and in-gap transports. In the in-band transport, the light field can tunnel through the lattices into the sink reservoir, and in the in-gap transport, the light field is self-trapped inside the lattices to form a solitary wave.

Elastic properties prediction of two- and three-dimensional multi-material lattices

Advances in multi-material additive manufacturing have opened unprecedented new opportunities for the design and manufacture of lightweight multifunctional structures. The ability to create complex topologies, at a relatively fine resolution, in addition to controlling the material composition on a voxel basis have significantly expanded the design space. To explore this large design space efficiently, accurate and cost-effective modeling tools are essential. In this paper, mechanics-based models for predicting the elastic properties of multi-material 2D and 3D lattice structures are developed or extended. The outcomes are compared with the predictions obtained from finite element models and experimental data. The results reveal that the adapted analytical models demonstrate good accuracy in predicting the elastic modulus of multi-material lattices for relative densities up to approximately 25 % while have considerably less computational cost compared to finite element using solid elements (providing the most accurate results in comparison with experiment). Careful consideration of the accuracy of the predictions is necessary for the use of these models for lattices with high relative density values. Besides, several homogenization-based models were studied to investigate their applicability to multi-material lattice structures when the assumption of scale-separation is considered valid. The capability of these models in predicting the whole elasticity tensor and the potential of multi-material lattices in manipulating the anisotropy are demonstrated. Finally, the introduced prediction frameworks are compared in order to provide an overview of their respective advantages and disadvantages in the case of multi-material lattice structures.

Topologically Defective Lattice Potential‐Based Gain‐Dissipative Ising Annealer with Large Noise Margin

AbstractGain‐dissipative Ising machines (GIMs) are annealers inspired by physical systems such as Ising spin glasses to solve combinatorial optimization problems. Compared to traditional quantum annealers, GIM is relatively easier to scale and can save on additional power consumption caused by low‐temperature cooling. However, traditional GIMs have a limited noise margin. Specifically, their normal operation requires ensuring that the noise intensity is lower than their saturation fixed point amplitude, which may result in increased power consumption to suppress noise‐induced spin state switching. To enhance the noise robustness of GIM, in this study a GIM based on a topologically defective lattice potential (TDLP) is proposed. Numerical simulations demonstrate that the TDLP‐based GIM can accurately simulate the bifurcation spin evolution in the Ising model. Furthermore, through the MAXCUT benchmark based on G‐set graphs, the optimal performance of TDLP‐based GIM is shown to surpass that of traditional GIMs. Additionally, the proposed TDLP‐based GIM successfully solves the MAXCUT benchmark and domain clustering dynamics benchmark based on G‐set graphs when the noise intensity exceeds its saturation fixed‐point amplitude. This indicates that the proposed system provides a promising architecture for breaking the small noise constraints required by traditional GIMs.

Soliton transformation in a cold Rydberg atomic system

This work presents a method for achieving soliton transformation in a cold Rydberg atomic system to enable the realization of diverse optical potentials. Our investigation demonstrates that this system can generate various solitons, including Gaussian, elliptical, ring, and necklace structures, based on different optical lattice potentials. Additionally, stable transitions from Gaussian profile to three other profiles can be achieved either abruptly or gradually by adjusting the centers and modulation depths of potentials along the direction of light propagation. These findings highlight the versatility of this system for generating and manipulating solitons. The ability to control soliton transformation offers prospects for various applications, including all-optical switching, optical information processing, and other areas.

Deterministic generation of highly squeezed GKP states in ultracold atoms

We demonstrate a method for encoding Gottesman–Kitaev–Preskill (GKP) error-correcting qubits with single ultracold atoms trapped in individual sites of a deep optical lattice. Using quantum optimal control protocols, we demonstrate the generation of GKP qubit states with 10 dB squeezing, which is the current minimum allowable squeezing level for use in surface code error correction. States are encoded in the vibrational levels of the individual lattice sites and generated via phase modulation of the lattice potential. Finally, we provide a feasible experimental protocol for the realization of these states. Our protocol opens up possibilities for generating large arrays of atomic GKP states for continuous-variable quantum information.

Exciton Localization Modulated by Ultradeep Moiré Potential in Twisted Bilayer γ-Graphdiyne.

Twisted moiré superlattice is featured with its moiré potential energy, the depth of which renders an effective approach to strengthening the exciton-exciton interaction and exciton localization toward high-performance quantum photonic devices. However, it remains as a long-standing challenge to further push the limit of moiré potential depth. Herein, owing to the pz orbital induced band edge states enabled by the unique sp-C in bilayer γ-graphdiyne (GDY), an ultradeep moiré potential of ∼289 meV is yielded. After being twisted into the hole-to-hole layer stacking configuration, the interlayer coupling is substantially intensified to augment the lattice potential of bilayer GDY up to 475%. The presence of lateral constrained moiré potential shifts the spatial distribution of electrons and holes in excitons from the regular alternating mode to their respective separated and localized mode. According to the well-established wave function distribution of electrons contained in excitons, the AA-stacked site is identified to serve for exciton localization. This work extends the materials systems available for moiré superlattice design further to serial carbon allotropes featured with benzene ring-alkyne chain coupling, unlocking tremendous potential for twistronic-based quantum device applications.

Collapse Dynamics of Vector Vortex Beams in Kerr Medium with Parity–Time-Symmetric Lattice Modulation

Based on the two-dimensional (2D) nonlinear Schrödinger equation, we investigate the collapse dynamics of a vector vortex optical field (VVOF) in nonlinear Kerr media with parity–time (PT)-symmetric modulation. The critical power for the collapse of a VVOF in a Kerr-ROLP medium (Kerr medium with a real optical lattice potential) is derived. Numerical simulations indicate that the number, position, propagation distance, and collapse profile of the collapse of a VVOF in sine and cosine parity–time-symmetric potential (SCPT) Kerr media are closely related to the modulation depth, initial powers, and the topological charge number of a VVOF. The VVOF collapses into symmetric shapes during propagation in a Kerr-ROLP medium, and collapse shapes are sensitively related to the density of the PT-symmetric optical lattice potential. In addition, due to gain–loss, the VVOF will be distorted during propagation in the Kerr-SCPT medium, forming an asymmetric shape of collapse. The power evolution of the VVOF in a Kerr-SCPT medium as a function of the transmission distance with different modulating parameters and topological numbers is analyzed in detail. The introduction of PT-symmetric optical lattice potentials into nonlinear Kerr materials may provide a new approach to manipulate the collapse of the VVOF.

Microscopic theory of nonlinear phase space filling in polaritonic lattices

We develop a full microscopic theory for a nonlinear phase space filling (NPSF) in strongly coupled two-dimensional polaritonic lattices. Ubiquitous in polaritonic experiments, the theoretical description of NPSF, also known as nonlinear optical saturation, remains limited to perturbative treatment and homogeneous samples. In this study, we go beyond the existing theoretical description and discover the broad scope of regimes where NPSF crucially modifies the optical response. Studying the quantum effects of non-bosonicity, cooperative light-matter coupling, and Coulomb blockade, we reveal several regimes for observing the nonlinear Rabi splitting quench due to the phase space filling. Unlike prior studies, we derive nonlinear Rabi frequency scaling all the way to the saturation limit and show that the presence of a lattice potential leads to qualitatively distinct nonlinearity. We concentrate on the three regimes of NPSF: (1) planar; (2) fractured; and (3) ultralocalized. For the planar saturation, the Rabi frequency decreases exponentially as a function of exciton density. For the fractured case, where excitons form a lattice with sites exceeding the exciton size, we discover fast NPSF at low occupations. This is followed by slower NPSF as the medium becomes fully saturated. This behavior is particularly pronounced in the presence of Coulomb (or Rydberg) blockade, where regions of fast and slow NPSF depend on the strength of repulsion. For the ultralocalized NPSF, we observe the square-root saturation typical to the collection of two-level systems. Our findings shed light on recent observations of strong nonlinearity in heterobilayers of transition metal dichalcogenides where moiré lattices emerge naturally []. Finally, the developed theory opens the prospects for engineering strongly nonlinear responses of polaritonic lattices with patterned samples, driving polaritonics into the quantum regime. Published by the American Physical Society 2024

Multipurpose platform for analog quantum simulation

Atom-based quantum simulators have had many successes in tackling challenging quantum many-body problems, owing to the precise and dynamical control that they provide over the systems' parameters. They are, however, often optimized to address a specific type of problem. Here, we present the design and implementation of a Li6-based quantum gas platform that provides wide-ranging capabilities and is able to address a variety of quantum many-body problems. Our two-chamber architecture relies on a robust combination of gray molasses and optical transport from a laser-cooling chamber to a glass cell with excellent optical access. There, we first create unitary Fermi superfluids in a three-dimensional axially symmetric harmonic trap and characterize them using thermometry, reaching temperatures below 20 nK. This allows us to enter the deep superfluid regime with samples of extreme diluteness, where the interparticle spacing is sufficiently large for direct single-atom imaging. Second, we generate optical lattice potentials with triangular and honeycomb geometry in which we study diffraction of molecular Bose-Einstein condensates, and show how going beyond the Kapitza-Dirac regime allows us to unambiguously distinguish between the two geometries. With the ability to probe quantum many-body physics in both discrete and continuous space, and its suitability for bulk and single-atom imaging, our setup represents an important step towards achieving a wide-scope quantum simulator. Published by the American Physical Society 2024

Exploring phononlike interactions in one-dimensional Bose-Fermi mixtures

With the objective of simulating the physical behavior of electrons in a dynamic background, we investigate a cold atomic Bose-Fermi mixture confined in an optical lattice potential solely affecting the bosons. The bosons, residing in the deep superfluid regime, inherit the periodicity of the optical lattice, subsequently serving as a dynamic potential for the polarized fermions. Owing to the atom-phonon interaction between the fermions and the condensate, the coupled system exhibits a Berezinskii-Kosterlitz-Thouless transition from a Luttinger liquid to a Peierls phase. However, under sufficiently strong Bose-Fermi interaction, the Peierls phase loses stability, leading to either a collapsed or a separated phase. We find that the primary function of the optical lattice is to stabilize the Peierls phase. Furthermore, the presence of a confining harmonic trap induces a diverse physical behavior, surpassing what is observed for either bosons or fermions individually trapped. Notably, under attractive Bose-Fermi interaction, the insulating phase may adopt a fermionic wedding-cake-like configuration, reflecting the dynamic nature of the underlying lattice potential. Conversely, for repulsive interaction, the trap destabilizes the Peierls phase, causing the two species to separate. Published by the American Physical Society 2024