Ladder Legs Research Articles

Synthetic Hall ladder with tunable magnetic flux

We describe a synthetic three-leg Hall ladder system with a tunable magnetic flux for neutral $^{173}\mathrm{Yb}$ atoms in a one-dimensional optical lattice. The ladder legs are formed by three hyperfine ground spin states of the atoms, and the complex interleg links are generated through Raman couplings between the spin states using multiple laser beams. The effective magnetic flux through a ladder plaquette $\ensuremath{\phi}$ is controlled by the angles of the Raman laser beams with the lattice axis. We investigate the quench dynamics of the Hall ladder system for $\ensuremath{\phi}\ensuremath{\approx}\frac{\ensuremath{\pi}}{3},\frac{\ensuremath{\pi}}{2},$ and $\frac{2\ensuremath{\pi}}{3}$ after a sudden application of the Raman coupling in various interleg link configurations. The semiclassical trajectory of the atoms in the plane of the spin composition and lattice position exhibits the characteristic motion of the effective magnetic field. In a tube configuration with the three legs cyclically linked, the quench evolution was observed to be substantially damped, which is attributed to the random flux threading the Hall tube.

Crystal-field approach to rare-earth higher borides: Dimerization, thermal, and magnetic properties ofRB50 (R=Tb,Dy,Ho,Er,Tm)

The microscopic justification for the dimerization in ladder-type rare-earth higher borides $R{\mathrm{B}}_{50}$ assumed by Mori [in Handbook on the Physics and Chemistry of Rare Earths, edited by K. A. Gschneidner, Jr., J.-C. G. B\unzli, and V. K. Pecharsky (North-Holland, Amsterdam, 2008), Vol. 38, p. 105] is presented. We consider a phenomenological model of crystal-field interactions and introduce Heisenberg antiferromagnetic exchange interactions between the rare-earth ions on the ladder rungs and the indirect exchange fields generated by magnetic interactions along the ladder legs. The crystal-field parameters and the exchange integrals for the rare-earth dimers are determined from modeling the temperature dependences of the heat capacity and static magnetic susceptibility. The field dependence of the low-temperature magnetization of polycrystalline samples of borides $R{\mathrm{B}}_{50}$ is simulated by making use of the proposed empirical expression for the renormalized magnetic moments of rare-earth ions. The characteristic anomalies of the thermal and magnetic properties of $\mathrm{Tb}{\mathrm{B}}_{50}, \mathrm{Dy}{\mathrm{B}}_{50}, \mathrm{Ho}{\mathrm{B}}_{50}$ and $\mathrm{Er}{\mathrm{B}}_{50}$ are successfully reproduced within the framework of this approach.

Magnetic field influence on kinetically-induced frustration in a hybrid spin-electron ladder

We study the influence of an external magnetic field in the ground-state and thermal spin correlations on a hybrid spin electron ladder. The model captures some characteristics of spin ladders present in a class of superconducting ceramics. It includes localized Ising spins and decorating mobile electrons. Ferromagnetic exchange couplings are assumed between neighboring spins. We show that the quantum kinetics, promoted by the hopping of decorating electrons between the ladder legs, induces antiferromagnetic correlations and magnetic frustration. The model is exactly solved using decoration–iteration transformation and transfer matrix techniques. In particular, we demonstrate that an external magnetic field promotes a reentrant character of the frustrated regime. The distinct ground-state orderings are also shown to be signaled by the magnetization curves as well as by the thermodynamic response functions.

Controlled parity switch of persistent currents in quantum ladders

We investigate the behavior of persistent currents for a fixed number of noninteracting fermions in a periodic quantum ladder threaded by Aharonov-Bohm and transverse magnetic fluxes $\mathrm{\ensuremath{\Phi}}$ and $\ensuremath{\chi}$. We show that the coupling between ladder legs provides a way to effectively change the ground-state fermion-number parity, by varying $\ensuremath{\chi}$. Specifically, we demonstrate that varying $\ensuremath{\chi}$ by $2\ensuremath{\pi}$ (one flux quantum) leads to an apparent fermion-number parity switch. We find that persistent currents exhibit a robust $4\ensuremath{\pi}$ periodicity as a function of $\ensuremath{\chi}$, despite the fact that $\ensuremath{\chi}\ensuremath{\rightarrow}\ensuremath{\chi}+2\ensuremath{\pi}$ leads to modifications of order $1/N$ of the energy spectrum, where $N$ is the number of sites in each ladder leg. We show that these parity-switch and $4\ensuremath{\pi}$ periodicity effects are robust with respect to temperature and disorder, and outline potential physical realizations using cold atomic gases and photonic lattices, for bosonic analogs of the effects.

Hidden Order and Symmetry Protected Topological States in Quantum Link Ladders.

We show that, whereas spin-1/2 one-dimensional U(1) quantum-link models (QLMs) are topologically trivial, when implemented in ladderlike lattices these models may present an intriguing ground-state phase diagram, which includes a symmetry protected topological (SPT) phase that may be readily revealed by analyzing long-range string spin correlations along the ladder legs. We propose a simple scheme for the realization of spin-1/2 U(1) QLMs based on single-component fermions loaded in an optical lattice with s and p bands, showing that the SPT phase may be experimentally realized by adiabatic preparation.

New metastable phases in an oxyborate compound obtained by an evolutionary algorithm and Density Functional Theory

New metastable phases in the Fe homometallic ludwigite compound are obtained and studied using an evolutionary algorithm and Density Functional Theory. Our lowest energy monoclinic structure is identified as P21/m with space group number of 11. This structure evolves towards the monoclinic structure as the result of the spin orbit coupling and a particular zigzag magnetic structure. A zigzag distortion in a class of three-leg ladders follows similar to the experimental one observed below the transition temperature of Tc=283K. In this distortion long and short bonds inside rungs alternating in a zigzag way along the ladder legs. Furthermore, a new type of zigzag structural ordering is observed in other two low-energy phases analyzed. In this case, the magnetic ordering behaves qualitatively similar to the experimental structure at 82K, with antiferromagnetically coupled ferromagnetic rungs. Our calculations show that magnetic symmetry is not favorable for zigzag structural ordering. Finally, structural and magnetic properties will be discussed in comparison with the experimentally known phases.

Electron spin resonance in a strong-rung spin-12Heisenberg ladder

Cu(C$_8$H$_6$N$_2$)Cl$_2$, a strong-rung spin-1/2 Heisenberg ladder compound, is probed by means of electron spin resonance (ESR) spectroscopy in the field-induced gapless phase above $H_{c1}$. The temperature dependence of the ESR linewidth is analyzed in the quantum field theory framework, suggesting that the anisotropy of magnetic interactions plays a crucial role, determining the peculiar low-temperature ESR linewidth behavior. In particular, it is argued that the uniform Dzyaloshinskii-Moriya interaction (which is allowed on the bonds along the ladder legs) can be the source of this behavior in Cu(C$_8$H$_6$N$_2$)Cl$_2$.

Locally tunable disorder and entanglement in the one-dimensional plaquette orbital model

We introduce a one-dimensional plaquette orbital model with a topology of a ladder and alternating interactions between $x$ and $z$ pseudospin components along both the ladder legs and on the rungs. We show that it is equivalent to an effective spin model in a magnetic field, with spin dimers that replace plaquettes and are coupled along the chain by three-spin interactions. Using perturbative treatment and mean field approaches with dimer correlations we study the ground state spin configuration and its defects in the lowest excited states. By the exact diagonalization approach we find that the quantum effects in the model are purely short-range and we get estimated values of the ground state energy and the gap in the thermodynamic limit from the system sizes up to $L=12$ dimers. Finally, we study a class of excited states with classical-like defects accumulated in the central region of the chain to find that in this region the quantum entanglement measured by the mutual information of neighboring dimers is locally increased and coincides with disorder and frustration. Such islands of entanglement in otherwise rather classical system may be of interest in the context of quantum computing devices.

Electronic structure and magnetic coupling in CaV2O5: spin dimer versus spin ladder

The electronic structure and magnetic exchange interactions of the ladder vanadate CaV2O5 have been studied by ab initio electronic structure calculations based on density functional theory (DFT). Geometry optimization and electronic structure calculations are performed using spin-polarized generalized gradient approximation (GGA) exchange-correlation functionals for four possible spin-ordered states. The experimentally observed insulating behavior has been reproduced successfully in the framework of the band theory by considering the magnetic ordering. Calculated results reveal that the true magnetic ground state of CaV2O5 is the antiferromagnetic (AFM) state with AFM exchange interactions both inside the rungs and along the ladder legs. Calculated exchange parameters indicate that the ladder structural vanadate CaV2O5 should be described as weakly coupled dimer system rather than as spin ladder compound. The AFM interactions inside the dimer are crucial to the insulating ground state and magnetic characteristics of CaV2O5.

First-principles study on the electronic structures of the ladder compound NaV2O4F

The electronic structures of ladder structural compound NaV2O4F are studied by first-principles calculations with pseudo-potential plane-wave method and spin-polarized generalized gradient approximation (GGA) based on density functional theory (DFT). Four possible spin-ordered states are simulated and the calculated results reveal that the magnetic ground state of NaV2O4F is the antiferromagnetic (AFM) state with AFM interactions both inside the rungs and along the ladder legs. The insulating behavior is successfully simulated with a band gap of about 1.0eV. According to crystal-field theory, the dxy orbitals of V atoms located in the VO4F pyramids have the lowest energy and are split from other d orbitals. The covalent interaction on the rungs becomes weak with the presence of F-ions. Using the calculated total energies for the various spin-ordered states of NaV2O4F, the spin exchange coupling constants are fit out with Noodleman's broken symmetry method. The calculated results indicate that there are ferromagnetic(FM) interactions between the ladders with competitive strength to that on the rungs and thereby NaV2O4F may not be a spin-ladder material.

Influence of structural modulations and the chain-ladder interaction in theSr14−xCaxCu24O41compounds

We studied the effects of the incommensurate structural modulations on the ladder subsystem of the ${\mathrm{Sr}}_{14\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ family of compounds using ab initio explicitly correlated calculations. From these calculations we derived $t\text{\ensuremath{-}}J$ model as a function of the fourth crystallographic coordinate $\ensuremath{\tau}$ describing the incommensurate modulations. It was found that in the highly calcium-doped system, the onsite orbital energies are strongly modulated along the ladder legs. On the contrary the two sites of the ladder rungs are isoenergetic and the holes are thus expected to be delocalized on the rungs. Chain-ladder interactions were also evaluated and found to be very negligible. The ladder superconductivity model for these systems is discussed in the light of the present results.

Nonlinear elasticity of anα-helical polypeptide: Monte Carlo studies

We report on Monte Carlo studies of the elastic properties of the helix-coil wormlike chain model of alpha-helical polypeptides. In this model the secondary structure enters as a scalar (Ising-like) variable that controls the local chain bending modulus. We characterize the nonlinear elastic properties of these molecules including their response to applied tensile forces and bending torques both individually and in combination. We find a pronounced effect of applied torque on the extensional compliance of the molecule and a similar effect of tension on the bending compliance. Finally we speculate that the strongly nonlinear response of alpha-helical polypeptides to combinations of torque and force plays a role in allosteric transitions in proteins.

Optimal sonar tactics over uncertain sediments

Tactical patterns for monostatic sensors were developed during the Cold War for deep, uniform underwater environments, where a simple median detection range defined a fixed spacing between search ladder legs. Acoustic conditions in littoral environments are so complex that spatial variability of bottom sediment properties destroys the simple homogeneous assumption associated with standard tactical search concepts. Genetic algorithms (GAs) have been applied to this problem to produce near-optimal, non-standard search tracks for monostatic mobile sensors that maximize probability of detection in such inhomogeneous environments. The present work describes a new capability called SPEAR (search planning with environmentally adaptive response) that adds tactical adaptation to search paths in a complex, littoral environment, as new in situ backscattering and bottom loss information becomes available. This presentation reviews the GA approach and discusses tactical adaptation to uncertain bottom sediment properties. The results show that easily implemented dynamic changes in active pulse depression angles and frequencies can produce significant improvement in detection performance in a complex littoral area. [Work supported by NAVSEA.]

Nonlinear model of intramolecular excitations on a multileg ladder lattice.

The exactly integrable model of nonlinear intramolecular excitations on a multileg ladder lattice is proposed. Since it is rather general, the model permits a number of physically interesting ramifications related to the striplike and the bunchlike biological and condensed matter systems as well as to the arrays of linearly and nonlinearly coupled optical fibers. The principal possibility to model an external magnetic field parallel to the ladder legs within the framework of inverse scattering transform is pointed out. The one-soliton solutions of two-leg and three-leg ladder models are found and analyzed. Apart from the spatially constricted translational mode typical to the traditional one-chain soliton, the interchain beating mode as well as the circular traveling modes redistributing the excitations between the chains are revealed in complete accordance with liner limits.

The Lists of Zerubbabel (Nehemiah 7 and Ezra 2) and the Hebrew Numeral Notation

parallel.' Ladder legs are well known from the thirteenth to the sixteenth dynasties and even in the eighteenth,2 and the cross patterns with bars between the intersecting horizontal and vertical lines are familiar enough, but nowhere has the writer been able to find anything which approximates this ladder motif at Beitin. There can be no doubt as to the date of the scarab impression. Its style conforms closely to that of the late Hyksos period.3 The design as a whole is a characteristic conventionalization of Egyptian signs, and has no particular meaning other than the word nefer, the symbol of excellence, fineness, or beauty. The owner, prompted by a belief in the efficacy of similars, may have felt that the scarab-impression would bring him good luck or at least ward off ill. In any event, to find a ladder at Bethel is unusual!