One-dimensional Lattice Research Articles

Continuous Time Randon Walks with Resetting in a Bounded Chain

The model of classical random walks with Poissonian resetting in a one-dimensional lattice is analyzed in detail in its general version. A special emphasis is made on the resetting effects that emerge due to the variety of arbitrary initial and boundary conditions. A quantum analog of the model is also discussed.

Designer topological flat bands in one-dimensional armchair graphene antidot lattices

Designer topological flat bands in one-dimensional armchair graphene antidot lattices

In Situ Subwavelength Microscopy of Ultracold Atoms Using Dressed Excited States

In this work, we implement a new method for imaging ultracold atoms with subwavelength resolution capabilities and determine its regime of validity. It uses the laser-driven interaction between excited states to engineer hyperfine ground-state population transfer in a three-level system on scales much smaller than the optical resolution. Subwavelength imaging of a quantum gas is atypical in the sense that the measurement itself perturbs the dynamics of the system. To avoid induced dynamics affecting the measurement, one usually “rapidly” measures the wave function in a so-called strong imaging regime. We experimentally illustrate this regime using a thermal gas ensemble, and demonstrate subwavelength resolution in quantitative agreement with a fully analytical model. Additionally, we show that, counterintuitively, the opposite weak imaging regime can also be exploited to reach subwavelength resolution. As a proof of concept, we demonstrate that this regime is a robust solution to select and spatially resolve a 30-nm-wide wave function, which was created and singled out from a tightly confined one-dimensional optical lattice. Using a general dissipation-included formalism, we derive validity criteria for both regimes. The formalism is applicable to other subwavelength methods. Published by the American Physical Society 2024

Helical Luttinger Liquid on a Space-Time Lattice.

The Luttinger model is a paradigm for the breakdown due to interactions of the Fermi liquid description of one-dimensional massless Dirac fermions. Attempts to discretize the model on a one-dimensional lattice have failed to reproduce the established bosonization results because of the fermion-doubling obstruction: a local and symmetry-preserving discretization of the Hamiltonian introduces a spurious second species of low-energy excitations, while a nonlocal discretization opens a single-particle gap at the Dirac point. Here, we show how to work around this obstruction by discretizing both space and time to obtain a local Lagrangian for a helical Luttinger liquid with Hubbard interaction. The approach enables quantum MonteCarlo simulations that preserve the topological protection of an unpaired Dirac cone.

Revealing discontinuous and continuous quantum phase transitions in shaken optical lattices

We perform the cluster mean-field with density matrix renormalization (CMFT+DMRG) calculation on the two-band extended Bose–Hubbard model to uncover the physics behind the discontinuous transitions observed in the one-dimensional shaken optical lattice with hybridized two lowest Bloch bands. We determine the superfluid, Mott insulator, and staggered superfluid phases associated with this model using the appropriate order parameters. We obtained the phase diagrams for two values of shaking amplitudes and illustrated the phases and nature of phase transitions. The transition from Mott insulator and superfluid to staggered superfluid is discontinuous for small shaking amplitudes. We analyse how the shaking frequency controls the effective chemical potential in the model and, consequently, the ground state energy that drives the discontinuous transition. Finally, we compare our results with those of earlier works.

Boundary-localized many-body bound states in the continuum

Bound states in the continuum (BICs), referring to spatially localized bound states with energies falling within the range of extended modes, have been extensively investigated in single-particle systems, leading to diverse applications in photonics, acoustics, and other classical-wave systems. Recently, there has been theoretical interest in exploring many-body BICs in interacting quantum systems, which necessitate the careful design of impurity potentials or spatial profiles of interaction. Here, we propose a type of many-body BICs localized at boundaries, which can be purely induced by the uniform onsite interaction without requiring any specific design of impurity potential or nonlocal interaction. We numerically show that three or more interacting bosons can concentrate on the boundary of a homogeneous one-dimensional lattice, which is absent at single- and two-particle counterparts. Moreover, the eigenenergy of multi-boson bound states can embed within the continuous energy spectra of extended scattering states, thereby giving rise to interaction-induced boundary many-body BICs. Furthermore, by mapping Fock states of three and four bosons to nonlinear circuit networks, we experimentally simulate boundary many-body BICs. Our findings enrich the comprehension of correlated BICs beyond the single-particle level, and have the potential to inspire future investigations on exploring many-body BICs.

Fate of localization features in a one-dimensional non-Hermitian flat-band lattice with quasiperiodic modulations

Fate of localization features in a one-dimensional non-Hermitian flat-band lattice with quasiperiodic modulations

Validity of an approximate electrostatic interaction model

We explain the reasons why a simple approximate expression for the interaction energy between two parallel uniformly charged wires works so well for the calculation of the stored electrostatic energy of a uniformly charged square and/or rectangular plate. The expression under consideration was also found to be very accurate when calculating the total energy of a model consisting of an arbitrary number of uniformly charged wires placed parallel to each other along a one-dimensional regular lattice when the number of wires is not very small. One can use the derived approximate expression for the interaction energy instead of the more elaborate exact one in all circumstances where there is no need for an extremely high accuracy.

Electro-Optic Response of Polymer-Stabilized Cholesteric Liquid Crystals with Different Polymer Concentrations.

Polymer-stabilized cholesteric liquid crystals (PSCLCs) have emerged as promising candidates for one-dimensional photonic lattices that enable precise tuning of the photonic band gap (PBG). This work systematically investigates the effect of polymer concentrations on the AC electric field-induced tuning of the PBG in PSCLCs, in so doing it explores a range of concentrations and provides new insights into how polymer concentration affects both the stabilization of cholesteric textures and the electro-optic response. We demonstrate that low polymer concentrations (≈3 wt. %) cause a blue shift in the short wavelength band edge, while high concentrations (≈10 wt. %) lead to a contraction and deterioration of the reflection band. Polarization optical microscopy was conducted to confirm the phase transition induced by the application of an electric field. The observations confirm that increased polymer concentration stabilizes the cholesteric texture. Particularly, the highly desired fingerprint texture was stabilized in a sample with 10 wt. % of the polymer, whereas it was unstable for lower polymer concentrations. Additionally, higher polymer concentrations also improved the dissymmetry factor and stability of the lasing emission, with the dissymmetry factor reaching the value of around 2 for samples with 10 wt. % of polymer additive. Our results provide valuable comprehension into the design of advanced PSCLC structures with tunable optical properties, enhancing device performance and paving the way for innovative photonic applications.

Continuous extension of the discrete shift translations on one-dimensional quantum lattice systems

We study the continuous extension of discrete shift translations on one-dimensional quantum lattice systems. We explore a specific example provided by a quasi-free C ∗ {C}^{\ast } -flow on the one-dimensional fermion lattice system, comparing it with its original discrete shift-translations. Specifically, we demonstrate its explicit dynamical formula, which reveals violations of causality and locality. Furthermore, we prove that this quasi-free C ∗ {C}^{\ast } -flow on the one-dimensional fermion lattice system cannot be extended to the one-dimensional quantum spin lattice system via the Jordan-Wigner transformation.

Power-law localization in one-dimensional systems with nonlinear disorder under fixed input conditions

We conduct a numerical investigation into wave propagation and localization in one-dimensional lattices subject to nonlinear disorder, focusing on cases with fixed input conditions. Utilizing a discrete nonlinear Schrödinger equation with Kerr-type nonlinearity and a random coefficient, we compute the averages and variances of the transmittance, T, and its logarithm, as functions of the system size L, while maintaining constant intensity for the incident wave. In cases of purely nonlinear disorder, we observe power-law localization characterized by 〈T〉∝L−γa and 〈lnT〉≈−γglnL for sufficiently large L. At low input intensities, a transition from exponential to power-law decay in 〈T〉 occurs as L increases. The exponents γa and γg are nearly identical, converging to approximately 0.5 as the strength of the nonlinear disorder, β, increases. Additionally, the variance of T decays according to a power law with an exponent close to 1, and the variance of lnT approaches a small constant as L increases. These findings are consistent with an underlying log-normal distribution of T and suggest that wave propagation behavior becomes nearly deterministic as the system size increases. When both linear and nonlinear disorders are present, we observe a transition from power-law to exponential decay in transmittance with increasing L when the strength of linear disorder, V, is less than β. As V increases, the region exhibiting power-law localization diminishes and eventually disappears when V exceeds β, leading to standard Anderson localization.

Numerical signatures of ultra-local criticality in a one dimensional Kondo lattice model

Heavy fermion criticality has been a long-standing problem in condensed matter physics. Here we study a one-dimensional Kondo lattice model through numerical simulation and observe signatures of local criticality. We vary the Kondo coupling J_KJK at fixed doping x. At large positive J_KJK, we confirm the expected conventional Luttinger liquid phase with 2k_F=\frac{1+x}{2}2kF=1+x2 (in units of 2\pi2π), an analogue of the heavy Fermi liquid (HFL) in the higher dimension. In the J_K ≤ 0JK≤0 side, our simulation finds the existence of a fractional Luttinger liquid (LL\star⋆) phase with 2k_F=\frac{x}{2}2kF=x2, accompanied by a gapless spin mode originating from localized spin moments, which serves as an analogue of the fractional Fermi liquid (FL\star⋆) phase in higher dimensions. The LL\star⋆ phase becomes unstable and transitions to a spin-gapped Luther-Emery (LE) liquid phase at small positive J_KJK. Then we mainly focus on the “critical regime” between the LE phase and the LL phase. Approaching the critical point from the spin-gapped LE phase, we often find that the spin gap vanishes continuously, while the spin-spin correlation length in real space stays finite and small. For a certain range of doping, in a point (or narrow region) of J_KJK, the dynamical spin structure factor obtained through the time-evolving block decimation (TEBD) simulation shows dispersion-less spin fluctuations in a finite range of momentum space above a small energy scale (around 0.035 J0.035J) that is limited by the TEBD accuracy. All of these results are unexpected for a regular gapless phase (or critical point) described by conformal field theory (CFT). Instead, they are more consistent with exotic ultra-local criticality with an infinite dynamical exponent z=+z=+. The numerical discovery here may have important implications on our general theoretical understanding of the strange metals in heavy fermion systems. Lastly, we propose to simulate the model in a bilayer optical lattice with a potential difference.

Critical regions in a one-dimensional flat band lattice with a quasi-periodic potential

In our previous work, the concept of critical region in a generalized Aubry–André model (Ganeshan–Pixley–Das Sarma’s model) has been established. In this work, we find that the critical region can be realized in a one-dimensional flat band lattice with a quasi-periodic potential. It is found that the above flat band lattice model can be reduced to an effective Ganeshan–Pixley–Das Sarma’s model. Depending on various parameter ranges, the effective quasi-periodic potential may be bounded or unbounded. In these two cases, the Lyapunov exponent, mobility edge, and critical indices of localized length are obtained exactly. In this flat band model, the localized-extended, localized-critical and critical-extended transitions can coexist. Furthermore, we find that near the transitions between the bound and unbounded cases, the derivative of Lyapunov exponent of localized states with respect to energy is discontinuous. At the end, the localized states in bounded and unbounded cases can be distinguished from each other by Avila’s acceleration.

Statistical description of interacting multistream quantum systems

In this research, the electrostatically coupled multistream quasiparticle excitations are studied in the framework of the Wigner distribution function. It is remarked that the Wigner distribution of coupled multistream collective quantum excitations satisfies a simple Liouville-like evolution equation from which a generalized distribution function for multistream quasiparticle excitations is deduced. The phase-space structure of collective quantum excitations in counter-stream electron and two-stream electron–positron gas with their evolution is calculated and electron/positron hole formation due to the onset of quantum stream instability is studied in connection with the energy band structure of the multistream quantum system, for the first time. The quantum stream instabilities in symmetric and asymmetric stream systems are studied and compared. It is found that the presence of opposite-charge streams leads to overall stability due to lowering the interaction potential effect. The generalized Wigner theory is also applied to study the electron transport in a one-dimensional periodic lattice using the concept of virtual streams. Current generalized statistical formalism may be used to model different quantum phenomena in the linear excitations limit with collective electrostatic interactions. The applications extend to the stream instability in quantum charge transport in metals, semiconductors, plasmonic devices, phase-space structure of charge carriers in periodic lattices interacting with the external potential of arbitrary shape and the dynamic evolution of dense electron–positron jets in active galactic nuclei or within the extremely dense astrophysical objects.

An efficient method to generate near-ideal hollow beams of different shapes for box potential of quantum gases.

Ultracold quantum gases are usually prepared in conservative traps for quantum simulation experiments. The atomic density inhomogeneity, together with the consequent position-dependent energy and time scales of cold atoms in traditional harmonic traps, makes it difficult to manipulate and detect the sample at a higher level. These problems are partially solved by optical box traps made of blue-detuned hollow beams. However, generating a high-quality hollow beam with high light efficiency for the box trap is challenging. Here, we present a scheme that combines the fixed optics, including axicons and prisms, to pre-shape a Gaussian beam into a hollow beam with a digital micromirror device (DMD) to improve the quality of the hollow beam further, providing a nearly ideal optical potential of various shapes for preparing highly homogeneous cold atoms. The highest power-law exponent of potential walls can reach a value over 100, and the light efficiency from a Gaussian to a hollow beam is also improved compared to direct optical shaping by a mask or a DMD. Combined with a one-dimensional optical lattice, a nearly ideal two-dimensional uniform quantum gas with different geometrical boundaries can be prepared for exploring quantum many-body physics to an unprecedented level.

Bound impurities in a one-dimensional Bose lattice gas: Low-energy properties and quench-induced dynamics

We study two mobile bosonic impurities immersed in a one-dimensional optical lattice and interacting with a bosonic bath. We employ the exact diagonalization method for small periodic lattices to study stationary properties and dynamics. We consider the branch of repulsive interactions that induce the formation of bound impurities, akin to the bipolaron problem. A comprehensive study of ground-state and low-energy properties is presented, including an examination of the interaction strengths which induce the formation of a bound dimer of impurities. We also study the dynamics induced after an interaction quench to examine the stability of the bound dimers. We reveal that after large interaction quenches from strong to weak interactions the system can show large oscillations over time with revivals of the dimer states. We find that the oscillations are driven by selected eigenstates with phase-separated configurations.

Clock-Line-Mediated Sisyphus Cooling.

We demonstrate subrecoil Sisyphus cooling using the long-lived ^{3}P_{0} clock state in alkaline-earth-like ytterbium. A 1388-nm optical standing wave nearly resonant with the ^{3}P_{0}→^{3}D_{1} transition creates a spatially periodic light shift of the ^{3}P_{0} clock state. Following excitation on the ultranarrow clock transition, we observe Sisyphus cooling in this potential, as the light shift is correlated with excitation to ^{3}D_{1} and subsequent spontaneous decay to the ^{1}S_{0} ground state. We observe that cooling enhances the loading efficiency of atoms into a 759-nm magic-wavelength one-dimensional (1D) optical lattice, as compared to standard Doppler cooling on the ^{1}S_{0}→^{3}P_{1} transition. Sisyphus cooling yields temperatures below 200nK in the weakly confined, transverse dimensions of the 1D optical lattice. These lower temperatures improve optical lattice clocks by facilitating the use of shallow lattices with reduced light shifts while retaining large atom numbers to reduce the quantum projection noise. This Sisyphus cooling can be pulsed or continuous and is applicable to a range of quantum metrology applications.

Periodic traveling waves of a SIR model with renewal and delay in one-dimensional lattice

This paper is primarily addressed to the (non)existence and asymptotic behaviors of periodic traveling waves for a SIR model with renewal and delay in one-dimensional lattice, which generalizes the conclusions of SIR models in one-dimensional continuous space. Especially, the challenge of establishing the asymptotic behaviors of periodic traveling waves when periodicity arises is solved by integral and analytic techniques. Moreover, the spreading speed is equal to the minimal wave speed can be obtained by our results.

One dimensional lattice fluid mixture with nearest neighbour interactions

We present an exact derivation of the free energy functional of a fluid mixture of hard rods with arbitrary sizes on a one-dimensional lattice. Our approach is based on the Wertheim cluster theory which consists of mapping a system with finite range interactions to the system with pure hard-core interaction but with modified activities. We show that the free energy functional has the same form as the fundamental measure functional. The interactions part of the free energy has two contributions, one from the one-particle cavity restricted to the hard rod or hard-sphere diameter and a second from the two-particle cavity which includes the finite range of the interaction. In the limit of a one-component system, our results reduce to the one derived using the Markov chain approach. For vanishing interactions, the density functionals coincide exactly with the previously derived for the mixture of hard rods with pure hard-core interaction.

Mean-chiral displacement in coherently driven photonic lattices and its application to synthetic frequency dimensions

Characterizing topologically nontrivial photonic lattices by measuring their topological invariants is crucial in topological photonics. In conservative one-dimensional systems, a widely used observable to extract the winding number is the mean-chiral displacement. In many realistic photonic systems, however, losses can hardly be avoided, and little is known on how one can extend the mean-chiral displacement to a driven-dissipative context. Here we theoretically propose an experimentally viable method to directly detect the topological winding number of one-dimensional chiral photonic lattices. The method we propose is a generalization of the mean-chiral displacement to a driven-dissipative context with coherent illumination. By integrating the mean-chiral displacement of the steady state over the pump light frequency, one can obtain the winding number with a correction of the order of the loss rate squared. We demonstrate that this method can be successfully applied to lattices along synthetic frequency dimensions.