Ladder Arrays Research Articles

Generalized and symmetric coprime planar array for direction of arrival estimation

Degrees of freedom and mutual coupling are two important factors to determine the ability of direction of arrival (DOA) estimation. Although coprime planar array (CPPA) has less mutual coupling than hourglass array (HA) and ladder array (LA), its positive and negative covariance corresponding lags are discontinuous, resulting in low degrees of freedom. In this study, we propose a generalized and symmetric coprime planar array (GSCA) by employing the symmetric property of the difference co-array. By moving one subarray and introducing a supplementary subarray, we construct a connected virtual uniform rectangular array (URA). Through further optimizing the sensor number, the redundant lags are reduced and the array structure is more general. We show that the degrees of freedom are much higher than those of CPPA, HA and LA. Besides, the mutual coupling is close to CPPA, but less than HA and LA. The superiority of GSCA is verified by simulations.

Fractional topological insulator precursors in spin-orbit fermion ladders

We study precursor states of fractional topological insulators (FTIs) in interacting fermionic ladders with spin-orbit coupling. Within a microscopically motivated bosonization approach, we investigate different competing phases depending on same-spin and interspin interactions at fractional effective filling $\nu=1/3$ per spin. In the spin-decoupled limit, we find that strong repulsive interactions of already moderate range may lead to a partially gapped state with two time-reversed copies of a quasi-one dimensional Laughlin phase. This FTI precursor competes with an interleg partially gapped phase displaying quasi long-range density wave order, however it may be stabilized if interactions have suitable anisotropy, or are sufficiently near SU($2$) symmetry, in leg space. When the FTI phase is present, it is moderately robust to small interspin interactions; these introduce competing partially gapped phases of orbital antiferromagnetic and bond density wave character. Performing a strong coupling analysis of the FTI precursor regime, we find that the main effect of interspin interactions is to induce correlated quasiparticle backscattering between the precursor FTI edge modes. Although this process competes with the topological phase, we show, by considering an array of ladders, that its influence may disappear upon approaching the two dimensional case. Considering time-reversal symmetry breaking perturbations, we also describe a protocol that adiabatically pumps $1/6$ charge per half-cycle, thus providing a quantized FTI signature arising already in the single ladder regime.

Propagation and Localization of Collective Excitations on a 24-Qubit Superconducting Processor.

Superconducting circuits have emerged as a powerful platform of quantum simulation, especially for emulating the dynamics of quantum many-body systems, because of their tunable interaction, long coherence time, and high-precision control. Here in experiments, we construct a Bose-Hubbard ladder with a ladder array of 20 qubits on a 24-qubit superconducting processor. We investigate theoretically and demonstrate experimentally the dynamics of single- and double-excitation states with distinct behaviors, indicating the uniqueness of the Bose-Hubbard ladder. We observe the linear propagation of photons in the single-excitation case, satisfying the Lieb-Robinson bounds. The double-excitation state, initially placed at the edge, localizes; while placed in the bulk, it splits into two single-excitation modes spreading linearly toward two boundaries, respectively. Remarkably, these phenomena, studied both theoretically and numerically as unique properties of the Bose-Hubbard ladder, are represented coherently by pairs of controllable qubits in experiments. Our results show that collective excitations, as a single mode, are not free. This work paves the way to simulation of exotic logic particles by subtly encoding physical qubits and exploration of rich physics by superconducting circuits.

A Cut-Resistant and Highly Restorable Graphene Foam.

High-pressure resistant and multidirectional compressible materials enable various applications but are often hindered by structure-derived collapse and weak elasticity. Here, a super-robust graphene foam with ladder shape microstructure capable of withstanding high pressure is presented. The multioriented ladder arrays architecture of the foam, consisting of thousands of identically sized square spaces, endow it with a great deal of elastic units. It can easily bear an iterative and multidirectional pressure of 44.5 MPa produced by a sharp blade, and may completely recover to its initial state by a load of 180 000 times their own weight even under 95% strain. More importantly, the foam can also maintain structural integrity after experiencing a pressure of 2.8 GPa through siphoning. Computational modeling of the "buckling of shells" mechanism reveals the unique ladder-shaped graphene foam contributes to the superior cut resistance and good resilience. Based on this finding, it can be widely used in cutting resistance sensors, monitoring of sea level, and the detection of oily contaminants in water delivery pipelines.

Extensions of Open Box Array With Reduced Mutual Coupling

Mutual coupling effect and degree of freedom are two important factors to be considered in the planar sparse array (PSA) design. This paper presents two new planar sparse geometries, referred to as the half H array and ladder array, by introducing the effective difference co-array concept and redistributing the dense array elements of the open box array (OBA) to the outer diagonal straight line. The detection capacities of the new structures can be maintained at the same level as the OBAs. Furthermore, they possess much fewer sensor pairs closely spaced, leading to the mutual coupling between the adjacent sensors significantly reduced. Simulations of the direction-of-arrival estimation verify the superiorities of the proposed PSAs with the 2-D unitary ESPRIT algorithm.

Interchangeable neck shape-specific coils for a clinically realizable anterior neck phased array system.

To demonstrate the interchangeable neck shape-specific (NSS) coil concept that supplements standard commercial spine and head/neck coils to provide simultaneous high-resolution (hi-res) head/neck imaging with high signal-to-noise ratio (SNR). Two NSS coils were constructed on formers designed to fit two different neck shapes. A 7-channel (7ch) ladder array was constructed on a medium neck former, and a 9-channel (9ch) ladder array was constructed on large neck former. Both coils were interchangeable with the same preamp housing. The 7ch and 9ch coils demonstrate SNR gains of approximately 4 times and 3 times over the Siemens 20-channel head/neck coil in the carotid arteries of our volunteers, respectively. Coupling between the Siemens 32-channel spine coil, Siemens 20-channel head/neck coil, and the NSS coils was negligible, allowing for simultaneous hi-res head/neck imaging with high SNR. This study demonstrates that supplementing existing commercial spine and head/neck coils with an NSS coil allows uniform simultaneous hi-res imaging with high SNR in the anterior neck, while maintaining SNR of the commercial coil in the head and posterior neck. Magn Reson Med 78:2460-2468, 2017. © 2017 International Society for Magnetic Resonance in Medicine.

Investigation of the Na Intercalation Mechanism into Nanosized V2O5/C Composite Cathode Material for Na-Ion Batteries.

There is a significant interest to develop high-performance and cost-effective electrode materials for next-generation sodium ion batteries. Herein, we report a facile synthesis method for nanosized V2O5/C composite cathodes and their electrochemical performance as well as energy storage mechanism. The composite exhibits a discharge capacity of 255 mAh g(-1) at a current density of 0.05 C, which surpasses that of previously reported layered oxide materials. Furthermore, the electrode shows good rate capability; discharge capacity of 160 mAh g(-1) at a current density of 1 C. The reaction mechanism of V2O5 upon sodium insertion/extraction is investigated using ex situ X-ray diffraction (XRD) and synchrotron based near edge X-ray absorption fine structure (NEXAFS) spectroscopy. Ex situ XRD result of the fully discharged state reveals the appearance of NaV2O5 as a major phase with minor Na2V2O5 phase. Upon insertion of sodium into the array of parallel ladders of V2O5, it was confirmed that lattice parameter of c is increased by 9.09%, corresponding to the increase in the unit-cell volume of 9.2%. NEXAFS results suggest that the charge compensation during de/sodiation process accompanied by the reversible changes in the oxidation state of vanadium (V(4+) ↔ V(5+)).

Bisdithiazolyl Radical Spin Ladders

A series of four bisdithiazolyl radicals 1a-d (R(1) = Pr, Bu, Pn, Hx; R(2) = F) has been prepared and characterized by X-ray crystallography. The crystal structure of 1a (R(1) = Pr) belongs to the tetragonal space group P42(1)m and consists of slipped π-stack arrays of undimerized radicals packed about 4 centers running along the z-direction, an arrangement identical to that found for 1 (R(1) = Et; R(2) = F). With increasing chain length of the R(1) substituent, an isomorphous set 1b-d is generated. All three compounds crystallize in the P2(1)/c space group and consist of pairs of radical π-stacks locked together by strong intermolecular F···S' bridges to create spin ladder arrays. The slipped π-stack alignment of radicals produces close S···S' interactions which serve as the "rungs" of a spin ladder, and the long chain alkyl substituents (R(1)) serve as buffers which separate the ladders from each other laterally. Variable temperature magnetic susceptibility measurements indicate that 1a behaves as an antiferromagnetically coupled Curie-Weiss paramagnet, the behavior of which may be modeled as a weakly coupled AFM chain. Stronger antiferromagnetic coupling is observed in 1b-d, such that the Curie-Weiss fit is no longer applicable. Analysis of the full data range (T = 2-300 K) is consistent with the Johnston strong-leg spin ladder model. The origin of the magnetic behavior across the series has been explored with broken-symmetry Density Functional Theory (DFT) calculations of individual pairwise exchange energies. These confirm that strong antiferromagnetic interactions are present within the ladder "legs" and "rungs", with only very weak magnetic exchange between the ladders.

Field theory for a fermionic ladder with generic intrachain interactions

An effective low energy field theory is developed for a system of two chains. The main novelty of the approach is that it allows to treat generic intrachain repulsive interactions of arbitrary strength. The chains are coupled by a direct tunneling and four-fermion interactions. At low energies the individual chains are described as Luttinger liquids with an arbitrary ratio of spin $v_s$ and charge $v_c$ velocities. A judicious choice of the basis for the decoupled chains greatly simplifies the description and allows one to separate high and low energy degrees of freedom. In a direct analogy to the bulk cuprates the resulting effective field theory distinguishes between three qualitatively different regimes: (i) small doping ($v_c << v_s$), (ii) optimal doping ($v_s \approx v_c$) and (iii) large doping ($v_s << v_c$). I discuss the excitation spectrum and derive expressions for the electron spectral function which turns out to be highly incoherent. The degree of incoherence increases when one considers an array of ladders (stripe phase).

Superconductivity generated by coupling to a cooperon in a two-dimensional array of four-leg Hubbard ladders

Starting from an array of four-leg Hubbard ladders weakly doped away from half-filling and weakly coupled by interladder tunneling, we derive an effective low-energy model which contains a partially truncated Fermi surface and a well-defined cooperon excitation formed by a bound pair of holes. An attractive interaction in the Cooper channel is generated on the Fermi surface through virtual scattering into the cooperon state. Although the model is derived in the weak coupling limit of a four-leg ladder array, an examination of exact results on finite clusters for the strong coupling $t\text{\ensuremath{-}}J$ model suggests the essential features are also present for a strong coupling Hubbard model on a square lattice near half-filling.

The d10 metal-sulfosalicylate complexes: Herring-bone, ladder and double-stranded chain frameworks with green luminescences

Assembly of 5-sulfosalicylic acid (H 3L) and d 10 transition metal ions (Cd II, Ag I) with the neutral N-donor ligands produces five new complexes: [Cd 2(HL) 2(4,4′-bipy) 3] n ·2 nH 2O ( 1), {[Cd 2( μ 2-HCO 2) 2(4,4′-bipy) 2(H 2O) 4][Cd(HL) 2(4,4′-bipy)(H 2O) 2]} n ( 2), {[Cd(4,4′-bipy)(H 2O) 4][HL]·H 2O} n ( 3), [Cd(HL)(dpp) 2(H 2O)] n ·4 nH 2O ( 4), {[Ag(4,4′-bipy)][Hhbs]} n ( 5) (4,4′-bipy=4,4′-bipyridine, dpp=1,3-di(pyridin-4-yl)propane, H 2hbs=4-hydroxybenzenesulfonic acid, the decarboxylation product of H 3L). Complex 1 adopts a 5-connected 3D bilayer topology. Complex 2 has the herring-bone and ladder chain, which are extended to a 3D network via hydrogen bonding. In 3–4 complexes, 3 is a 3D supermolecular structure formed by polymeric chains and 2D network of HL 2−, while 4 gives the double-stranded chains. In 5, ladder arrays are stacked with the 2D networks of Hhbs − anions in an –ABAB– sequence. Complexes 1–4 display green luminescences in solid state at room temperature, while emission spectra of 3 and 4 show obvious blue-shifts at low temperature.

A phenomenological theory of the pseudogap state

An ansatz is proposed for the coherent part of the single particle Green’s function in a doped resonant valence bond (RVB) state by analogy with the form derived by Konik and coworkers for an array of 2-leg Hubbard ladders near half-filling. The parameters of the RVB state are taken from the renormalized mean field theory of Zhang and coworkers for underdoped cuprates. The ansatz shows good agreement with recent angle resolved photoemission on underdoped cuprates and resolves an apparent disagreement with the Luttinger sum rule.

Strong Cooperative Enhancement of Two-Photon Absorption in Double-Strand Conjugated Porphyrin Ladder Arrays

We present the two-photon absorption (2PA) spectra of a series of conjugated porphyrin oligomers containing N = 2, 4, 8, and ca. 13 monomer units, meso-meso connected with butadiyne linkers. We demonstrate that, in the coplanar double-strand arrays, self-assembled upon addition of 4,4'-bipyridyl, the conjugation length increases dramatically, leading to very strong cooperative enhancement of 2PA. We analyze the scaling of 2PA in both the double-strand and rotationally free single-strand arrays and show how the effective conjugation length in both cases is linked to the observed 2PA properties. By introducing a "conjugation signature" for the 2PA strength, we show that, in double-strand arrangement, the conjugation embraces the whole molecule up to the tetramer level, whereas in single-strand arrangement, it is always less than N, except for N = 2, but keeps increasing until N = 8. Our finding of extremely strong 2PA cross section, sigma2 approximately 105 GM, in double-strand oligomers peaking at 1.3 mum can find use for signal processing in fiber-optic devices.

Phenomenological theory of the pseudogap state

An ansatz is proposed for the coherent part of the single particle Green's function in a doped resonant valence bond (RVB) state by analogy with the form derived by Konik and co-workers for a doped spin liquid formed by an array of two-leg Hubbard ladders near half-filling. The parameters of the RVB state are taken from the renormalized mean field theory of Zhang and co-workers for underdoped cuprates. The ansatz shows good agreement with recent angle resolved photoemission on underdoped cuprates and resolves an apparent disagreement with the Luttinger sum rule. The transition in the normal state from a doped RVB spin liquid to a standard Landau Fermi liquid, that occurs in the renormalized mean field theory, appears as a quantum critical point characterized by a change in the analytic form of the Green's function. A $d$-wave superconducting dome surrounding this quantum critical point is introduced phenomenologically. Results are also presented for the Drude weight and tunneling density of states as functions of the hole density.

Extended lanthanide–transition metal arrays with cyanide bridges: syntheses, structures, and catalytic applications

Systematic synthetic procedures produced several different structural types of extended lanthanide–transition metal (group 10) complexes with cyanide bridges. Of these, one-dimensional ladder arrays containing a Yb–Pd combination have been converted to bimetallic heterogeneous catalysts on an oxide (SiO 2) surface that is more effective than supported Pd alone. Two lanthanide–Cu(I) complexes have been prepared. One type, an inclusion complex consists of lanthanide(III) cations encapsulated in the pockets of a three-dimensional anionic array that contains Cu(I)–CN–Cu(I) bridges. The second type, an extended layer complex, consists of joined five-membered rings in a “tile-like” pattern with Ln–CN–Cu and Cu–CN–Cu bridges.

Synchronization in disordered Josephson junction arrays: Small-world connections and the Kuramoto model

We study synchronization in disordered arrays of Josephson junctions. In the first half of the paper, we consider the relation between the coupled resistively and capacitively shunted junction (RCSJ) equations for such arrays and effective phase models of the Winfree type. We describe a multiple-time-scale analysis of the RCSJ equations for a ladder array of junctions with non-negligible capacitance in which we arrive at a second order phase model that captures well the synchronization physics of the RCSJ equations for that geometry. In the second half of the paper, motivated by recent work on small-world networks, we study the effect on synchronization of random, long-range connections between pairs of junctions. We consider the effects of such shortcuts on ladder arrays, finding that the shortcuts make it easier for the array of junctions in the nonzero voltage state to synchronize. In two-dimensional (2D) arrays we find that the additional shortcut junctions are only marginally effective at inducing synchronization of the active junctions. The differences in the effects of shortcut junctions in 1D and 2D can be partly understood in terms of an effective phase model.

Suppression of the charge-density-wave state in Sr14Cu24O41 by calcium doping.

The charge response in the spin chain and/or ladder compound Sr14-xCaxCu24O41 is characterized by dc resistivity, low-frequency dielectric spectroscopy and optical spectroscopy. We identify a phase transition below which a charge-density wave (CDW) develops in the ladder arrays. Calcium doping suppresses this phase with the transition temperature decreasing from 210 K for x=0 to 10 K for x=9, and the CDW gap from 130 meV down to 3 meV, respectively. This suppression is due to the worsened nesting originating from the increase of the interladder tight-binding hopping integrals, as well as from disorder introduced at the Sr sites. These results altogether speak in favor of two-dimensional superconductivity under pressure.

Synchronization of coupled rotators: Josephson junction ladders and the locally coupled Kuramoto model.

We show that the resistively shunted junction (RSJ) equations describing a ladder array of overdamped, critical-current disordered Josephson junctions that are current biased along the rungs of the ladder can be mapped onto a Kuramoto model with nearest neighbor, sinusoidal couplings. This result is obtained by an averaging method, in which the fast dynamics of the RSJ equations are integrated out, leaving the dynamics which describe the time scale over which neighboring junctions along the rungs of the ladder phase and frequency synchronize. We quantify the degree of frequency synchronization of the rung junctions by calculating the standard deviation of their time-averaged voltages, sigma(omega), and the phase synchronization is quantified by calculating the time average of the modulus of the Kuramoto order parameter, <|r|>. We test the results of our averaging process by comparing the values of sigma(omega) and <|r|> for the original RSJ equations and our averaged equations. We find excellent agreement for dc bias currents of I(B)/<I(c)> greater, similar 3, where <I(c)> is the average critical current of the rung junctions, and critical current disorders of up to 10%. We also study the effects of thermal noise on the synchronization properties of the overdamped ladder. Finally, we find that including the effects of junction capacitance can lead to a discontinuous synchronization transition as the strength of the coupling between neighboring junctions is smoothly varied.

Interactions between Josephson vortices and breathers

We study vortex-breather collisions in a Josephson-junction ladder array. We have computed parameters values of the system for which both types of structures coexist in the ladder. In order of increasing bias current, we have found different possible scenarios for vortex-breather collisions. (i) At low bias current, the breather acts as a pinning center for a single vortex. (ii) Increasing the current, the vortex excites multisite breathers in its wake and is finally pinned by the breather. (iii) At still higher current, a whirling mode front is excited by the vortex. However, the breather still acts as a pinning center, but now for the front. (iv) At higher values of the bias, the front is able to destroy the breather. For scenario (i), we have also studied thermal activation properties associated with the presence of the vortex-breather pair in the array.

Phase locking in Josephson ladders and the discrete sine-Gordon equation: the effects of boundary conditions and current-induced magnetic fields.

We report on the stability of phase-locked solutions to ladder arrays of underdamped Josephson junctions under both periodic and open boundary conditions and in the presence of current-induced magnetic fields. We calculate the Floquet exponents based on the resistively and capacitively shunted junction (RCSJ) model, as well as on a simplified model of the ladder that leads to a discrete sine-Gordon (DSG) equation for the horizontal, current-biased junctions. In the case of zero induced magnetic fields, we find the DSG equation (commonly applied to parallel arrays) appreciably overestimates the exponents of the full ladder in the overdamped regime (corresponding to the limit of small junction capacitance, beta(c)), and that difference physically results from differing spectra for small-amplitude phase oscillations of the DSG and RCSJ equations. mutual inductance between plaquettes is included we find there are ranges of values for the mutual inductance for which the ladder is in fact unstable. To understand the cause of the observed instabilities, it is crucial to consider the behavior of the vertical junctions.