One-dimensional Lattice Research Articles

Dipole–monopole alternative as the precursor of pseudo-excitonic chargeless half-mode in an integrable nonlinear exciton–phonon system on a regular one-dimensional lattice

The new form of an integrable exciton–phonon nonlinear dynamical system distinguished by the two physical parameters is suggested. The system is settled along an infinite one-dimensional regular lattice and it admits the semi-discrete Lax representation in terms of 3 × 3 auxiliary spectral and evolution matrices. The explicit analytical four-component solution to the system’s dynamical equations found by means of Darboux–Bäcklund dressing technique turns out to be of broken PT-symmetry giving rise to the crossover between the monopole and dipole regimes of system’s dynamics. The crossover effect is proved to be inseparable from the mutual influence between the interacting subsystems in the form of specific nonlinear superposition of two qualitatively distinct types of traveling waves characterized by the two spatial scales and by the two velocities of two physically distinct origins. The threshold value of localization parameter separating the monopole and dipole dynamical regimes is strictly established in terms of the basic physical parameters. The phenomenon of dipole–monopole alternative for the spatial distribution of pseudo-excitons is shown to initiate the partial splitting between the pseudo-excitonic and vibrational subsystems in the so-called threshold dynamical regime specified by the threshold value of localization parameter. This partial splitting is manifested by the complete elimination of one pseudo-excitonic component accompanied by the actual conversion of another pseudo-excitonic component into the pseudo-excitonic chargeless half-mode. Relying upon the inherent PT-symmetry of system’s dynamical equations the four-component symmetry broken PT-conjugated counterpart solution is also analytically recovered. The integrable nonlinear exciton–phonon system under study is expected to be useful in modeling the nonlinear dynamical properties of PT-symmetric metamaterials. The critical overviews of several relevant and several irrelevant model systems are given to rebuff certain misleading but dogmatically accepted notions and statements circulating in scientific literature.

Topological Frenkel exciton polaritons in one-dimensional lattices of strongly coupled cavities

Frenkel polaritons, hybrid light-matter quasiparticles, offer promise for the designing of new optoelectronic devices. However, their technological implementations are hindered by sensitivity to imperfections. Topology has been raised as a way to circumvent defects and fabrication limitations. Here, we propose a lattice of cavities to realize the one-dimensional Su-Schrieffer-Heeger model (SSH) for topological Frenkel polaritons. By engineering the configuration of the cavities we demonstrate that the SSH topological and trivial phases can be accessed, which we unravel by employing a dual approach based on classical and quantum theories. We study the role of inherent vibron modes and fabrication defects in the robustness of the topological phases of polaritons. Our study demonstrates a simple experimentally realistic setup to realize topological polaritons at room temperature.

One-dimensional symmetric phases protected by frieze symmetries

We make a systematic study of symmetry-protected topological gapped phases of quantum spin chains in the presence of the frieze space groups in one dimension using matrix product states. Here, the spatial symmetries of the one-dimensional lattice are considered together with an additional ``vertical reflection,'' which we take to be an on-site ${\mathbb{Z}}_{2}$ symmetry. We identify seventeen distinct non-trivial phases, define canonical forms, and compare the topological indices obtained from the MPS analysis with the group cohomological predictions. We furthermore construct explicit renormalization group fixed-point wave functions for symmetry-protected topological phases with global on-site symmetries, possibly combined with time reversal and parity symmetry. En route, we demonstrate how group cohomology can be computed using the Smith normal form.

Two-particle topological Thouless spin pump

We show that two particles interacting via spin exchange exhibit topological features found in one-dimensional single particle lattice models. This is accomplished by absorbing all of the spatial degrees of freedom of the lattices into the spin degrees of freedom of the two particles. Comparing the spin system with the Su-Schrieffer-Heeger model, we show the existence of topologically protected edge spin states and establish the bulk-edge correspondence. Modifying the spin system with a chiral symmetry breaking term results in it resembling the Rice-Mele model and can therefore act as a Thouless spin pump of one of the particles when periodically and adiabatically driven. By using the spin states as a synthetic spatial dimension, we show two particles are enough to simulate well known topological properties in condensed matter physics.

Uncertainty quantification in inerter-based quasiperiodic lattices

Inerter-based periodic structures have attracted significant interest among the research community due to their wide range of applications. However, existing studies on quasiperiodic structures, especially with inerters, are limited. Therefore, this timely work investigates the dynamics of novel one-dimensional inerter-based quasiperiodic lattices with and without local resonators. The quasiperiodicity is introduced through the modulation of both spring and inerter properties resulting in the well-known Hofstadter-like butterfly spectrum having a fractal structure. Moreover, by considering the appropriate boundary conditions and many mass–spring-inerter subsystems, the bulk spectrum of the system is investigated demonstrating the existence of multiple edge states in lower and higher frequency ranges. The deterministic study showed that the effect of inertia amplification is to reduce the frequencies of the Hofstadter-like butterfly and to widen the low frequency band gaps. The second contribution of this work involves investigating the effect of parametric uncertainty for the acoustic-metamaterial-like chain based on Monte Carlo simulations. Moreover, to address the computational aspect of the problem, grey-box modeling using machine learning was performed. A Gaussian process model was trained on a limited dataset and was found to capture the stochastic responses of the lattices adequately. The statistical variation of parameters with different levels of uncertainty demonstrated significant effects on the Hofstadter-like butterfly, band gaps, corresponding edge states and frequency responses. The sensitivity of the dynamic behavior in quasiperiodic lattices to variabilities reveal the need to account for system uncertainties for their targeted performance as future vibration absorbers and energy harvesters. The study also paves the way to utilize the results as useful prior information for robust design optimization of real inerter-based quasiperiodic lattice devices.

Energy polarization and energy pumping in Rice-Mele chains

The one-dimensional Rice-Mele lattice consisting of two-site unit cells enables topological charge pumping at low enough temperatures. We show here that energy pumping is feasible in this system. We analyze energy polarization using the second-quantization formalism and connect it to intercell energy current by the relevant continuity equation. Following this formulation, we numerically evaluate the energy current pumped in an adiabatic cycle when the system parameters vary periodically and slowly with time. Unlike the pumped charge, the pumped energy is entirely temperature-independent at half filling. The global Berry phase for all bands and the related topological phase transitions during the pumping cycle account for the energy pumping. The present study paves the way for manipulating energy current without electric and thermal biases.

Source-driven homogenization theory for electro-momentum coupled scatterers

Willis materials are metamaterials whose subwavelength asymmetry couples the macroscopic pressure-strain and momentum-velocity relations. Recently, the design space of these metamaterials has been expanded to consider asymmetric piezoelectric scatterers and thereby couple the electric field-electric displacement relation to the constitutive equations in the Willis form. The existence of this so-called electro-momentum coupling was first predicted using dynamic homogenization of heterogeneous piezoelectric media [J. Mech. Phys. Solids 134, 103770 (2020)] but it can also be understood through a generalized polarizability tensor α that calculates the electro-acoustic field scattered from a single asymmetric piezoelectric inhomogeneity as a function of local fields [Proc. Mtgs. Acoust. 46, 065002 (2022)]. We present a multiple-scattering dynamic homogenization method that extends the work of Sieck et al. [Phys. Rev. B 96, 104303 (2017)] using the generalized polarizability tensor. The model considers the microscale scattered pressure, velocity, and electric fields in a one-dimensional periodic lattice of identical scatterers to find analytical expressions for the effective macroscale fields. The macroscale fields are then used to find the effective electro-momentum coupling constants in terms of the polarizability of the individual scatterers and the concentration of scatterers in a background medium. [Work supported by DARPA and ARL:UT McKinney Fellowship in Acoustics.]

Artificial neural network for the single-particle localization problem in quasiperiodic one-dimensional lattices

The use of machine learning algorithms to address classification problems in several scientific branches has increased over the past years. In particular, the supervised learning technique with artificial neural networks has been successfully employed in classifying phases of matter. In this article, we use a fully connected feed-forward neural network to classify extended and localized single-particle states that arise from quasiperiodic one-dimensional lattices. We demonstrate that our neural network achieves to correctly uncover the nature of the single-particle states even when the wave functions come from a more complex Hamiltonian than the one used to train the network.

The Effect of On-Site Potentials on Supratransmission in One-Dimensional Hamiltonian Lattices.

We investigated a class of one-dimensional (1D) Hamiltonian N-particle lattices whose binary interactions are quadratic and/or quartic in the potential. We also included on-site potential terms, frequently considered in connection with localization phenomena, in this class. Applying a sinusoidal perturbation at one end of the lattice and an absorbing boundary on the other, we studied the phenomenon of supratransmission and its dependence on two ranges of interactions, 0<α<∞ and 0<β<∞, as the effect of the on-site potential terms of the Hamiltonian varied. In previous works, we studied the critical amplitude As(α,Ω) at which supratransmission occurs, for one range parameter α, and showed that there was a sharp threshold above which energy was transmitted in the form of large-amplitude nonlinear modes, as long as the driving frequency Ω lay in the forbidden band-gap of the system. In the absence of on-site potentials, it is known that As(α,Ω) increases monotonically the longer the range of interactions is (i.e., as α⟶0). However, when on-site potential terms are taken into account, As(α,Ω) reaches a maximum at a low value of α that depends on Ω, below which supratransmission thresholds decrease sharply to lower values. In this work, we studied this phenomenon further, as the contribution of the on-site potential terms varied, and we explored in detail their effect on the supratransmission thresholds.

Fate of the reentrant localization phenomenon in the one-dimensional dimerized quasiperiodic chain with long-range hopping

Recently, the exciting reentrant localization transition phenomenon was found in a one-dimensional dimerized lattice with staggered quasiperiodic potentials. Usually, long-range hopping is typically important in actual physical systems. In this work, we study the effect of next-nearest neighbor hopping (NNNH) on the reentrant localization phenomenon. Due to the presence of NNNH, the broken chiral symmetry is further enhanced and the localization properties of electron states in the upper and lower bands become quite different. It is found that the reentrant localization can still persist within a range of NNNH both in Hermitian and non-Hermitian cases. Eventually, the reentrant localization disappears as the strength of NNNH increases to some extent, since the increasing NNNH weakens the dimerization of the system and destroys its competition with the quasiperiodic disorder. Our work thus reveals the effect of long-range hopping in the reentrant localization phenomenon and deepens its physical understanding.

Machine learning matrix product state ansatz for strongly correlated systems.

Machine learning (ML) has been used to optimize the matrix product state (MPS) ansatz for the wavefunction of strongly correlated systems. The ML optimization of MPS has been tested for the Heisenberg Hamiltonian on one-dimensional and ladder lattices, which correspond to conjugated molecular systems. The input descriptors and output for the supervised ML are lattice configurations and configuration interaction coefficients, respectively. Efficient learning can be achieved from data over the full Hilbert space via exact diagonalization or full configuration interaction, as well as over a much smaller sub-space via Monte Carlo Configuration Interaction. We show that this circumvents the need to calculate energy and operator expectation values and is therefore a computationally efficient alternative to variational optimization.

Observation of the Sign Reversal of the Magnetic Correlation in a Driven-Dissipative Fermi Gas in Double Wells.

We report the observation of the sign reversal of the magnetic correlation from antiferromagnetic to ferromagnetic in a dissipative Fermi gas in double wells, utilizing the dissipation caused by on-site two-body losses in a controlled manner. We systematically measure dynamics of the nearest-neighbor spin correlation in an isolated double-well optical lattice, as well as a crossover from an isolated double-well lattice to a one-dimensional uniform lattice. In a wide range of lattice configurations over an isolated double-well lattice, we observe a ferromagnetic spin correlation, which is consistent with a Dicke type of correlation expected in the long-time limit. This work demonstrates the control of quantum magnetism in open quantum systems with dissipation.

Mobile impurities interacting with a few one-dimensional lattice bosons

We report a comprehensive study of the ground-state properties of one and two bosonic impurities immersed in small one-dimensional optical lattices loaded with a few interacting bosons. We model the system with a two-component Bose–Hubbard model and solve the problem numerically by means of the exact diagonalization method. We report binding energies of one and two impurities across the superfluid (SF) to Mott-insulator transition and confirm the formation of two-body bound states of impurities induced by repulsive interactions. In particular, we found that an insulator bath induces tightly bound di-impurity dimers, whereas a SF bath induces shallower bound states.

Transport of ultracold atoms in superpositions of S - and D -band states in a moving optical lattice

Ultracold atoms in a moving optical lattice with high controllability are a feasible platform to research the transport phenomenon. Here, we study the transport process of ultracold atoms at the $D$ band in a one-dimensional optical lattice and manipulate the transport of superposition states with different superposition weights of $S$-band and $D$-band atoms. In the experiment, we first load ultracold atoms into an optical lattice using the shortcut method and then accelerate the optical lattice by scanning the phase of lattice beams. The atomic transport at the $D$ band and $S$ band is demonstrated, respectively. The group velocity of atoms at the $D$ band is opposite to that at the $S$ band. By preparing superposition states with different superposition weights of the $D$-band and $S$-band atoms, we realize the manipulation of atomic group velocity from positive to negative, and observe the quantum interference between atoms at different bands. The influence of the lattice depth and acceleration on the transport process is also studied. Moreover, the multiorbital simulations are coincident with the experimental results. Our paper sheds light on the transport process of ultracold atoms at higher bands in optical lattices and provides a useful method to manipulate the transport of atomic superposition states.

Controlled quantized adiabatic transport in a superlattice Wannier-Stark ladder

The Born–Fock theorem is one of the most fundamental theorems of quantum mechanics and forms the basis for reliable and efficient navigation in the Hilbert space of a quantum system with a time-dependent Hamiltonian by adiabatic evolution. In the absence of level crossings, i.e. without degeneracies, and under adiabatic time evolution all eigenstates of the Hamiltonian keep their energetic order, labeled by a conserved integer quantum number. Thus, controlling the eigenstates of the Hamiltonian and their energetic order in asymptotic limits allows one to engineer a perfect adiabatic transfer between a large number of initial and target states. The fidelity of the state transfer is only limited by adiabaticity and the selection of target states is controlled by the integer invariant labeling the order of eigenstates. We show here, for the example of a finite superlattice Wannier-Stark ladder, i.e. a one-dimensional lattice with alternating hopping amplitudes and constant potential gradient, that such an adiabatic control of eigenstates can be used to induce perfectly quantized single-particle transport across a pre-determined number of lattice sites. We dedicate this paper to the memory of our late friend and colleague Bruce Shore, who was an expert in adiabatic processes and taught us much about this field.

Asymtotic of the Discrete Spectrum of the Three-Particle Schrödinger Operator on a One-Dimensional Lattice

Asymtotic of the Discrete Spectrum of the Three-Particle Schrödinger Operator on a One-Dimensional Lattice

Simulating the Hamiltonian of dimer atomic spin model of one-dimensional optical lattice on quantum computers

The one-dimensional Ising model with its connections to several physical concepts plays a vital role in comprehension of several principles, phenomena and numerical methods. The Hamiltonian of a coupled one-dimensional dissipative spin system in the presence of magnetic field can be obtained from the Ising model. We simulate the above Hamiltonian by designing a quantum circuit with precise gate measurement and execute with the IBMQ experience platform through different [Formula: see text] states with controlled energy separation where we can check quantum synchronization in a dissipative lattice system. Our result shows the relation between various entangled states, the relation between the different energy separation ([Formula: see text]) with the spin–spin coupling ([Formula: see text]) in the lattice, along with fidelity calculations for several iterations of the model used. We also estimate the ground and first excited energy states of Ising-Hamiltonian using VQE algorithm and investigate the lowest energy values varying the number of layers of ansatz.

Skeleton structure inherent in discrete-time quantum walks

In this paper, we claim that a common underlying structure--a skeleton structure--is present behind discrete-time quantum walks (QWs) on a one-dimensional lattice with a homogeneous coin matrix. This skeleton structure is independent of the initial state, and partially, even of the coin matrix. This structure is best interpreted in the context of quantum-walk-replicating random walks (QWRWs), i.e., random walks that replicate the probability distribution of quantum walks, where this newly found structure acts as a simplified formula for the transition probability. Additionally, we construct a random walk whose transition probabilities are defined by the skeleton structure and demonstrate that the resultant properties of the walkers are similar to both the original QWs and QWRWs.

Dimensional cross-over in self-organised super-radiant phases of ultra-cold atoms inside a cavity

We consider a condensate of ultra-cold bosonic atoms in a linear optical cavity illuminated by a two-pump configuration where each pump makes different angles with the direction of the cavity axis. We show that such a configuration allows a smooth transition from a one-dimensional quantum optical lattice configuration to a two-dimensional quantum optical lattice configuration induced by the cavity–atom interaction. Using a Holstein–Primakoff transformation, we find the atomic density profile of such a self-organised ground state in the super-radiant phase as a function of the angular orientations of the pumps in such a dynamical quantum optical lattice, and also provide an analysis of their structures in coordinate and momentum space. In the later part of the paper, we show how the corresponding results can also be qualitatively understood in terms of an extended Bose–Hubbard model in such a quantum optical lattice potential.

Rogue waves in quantum lattices with correlated disorder

We investigate the outbreak of anomalous quantum wave-function amplitudes in a one-dimensional tight-binding lattice featuring correlated diagonal disorder. Such rogue-wave-like behavior is fostered by a competition between localization and mobility. The effective correlation length of the disorder is ultimately responsible for bringing the local disorder strength to a minimum, fueling the occurrence of extreme events of much higher amplitudes, especially when compared to the case of uncorrelated disorder. Our findings are valid for a class of discrete one-dimensional systems and reveal profound aspects of the role of randomness in rogue-wave generation.