Optimized Dynamical Decoupling for Time Dependent Hamiltonians

The validity of optimized dynamical decoupling (DD) is extended to analytically time dependent Hamiltonians. As long as an expansion in time is possible the time dependence of the initial Hamiltonian does not affect the efficiency of optimized dynamical decoupling (UDD, Uhrig DD). This extension provides the analytic basis for (i) applying UDD to effective Hamiltonians in time dependent reference frames, for instance in the interaction picture of fast modes and for (ii) its application in hierarchical DD schemes with $\pi$ pulses about two perpendicular axes in spin space. to suppress general decoherence, i.e., longitudinal relaxation and dephasing.Comment: 5 pages, no figure

Magnetic Properties of (VO)_2P_2O_7 from Frustrated Interchain Coupling

Neutron-scattering experiments on (VO)_2P_2O_7 reveal both a gapped magnon dispersion and an unexpected, low-lying second mode. The proximity and intensity of these modes suggest a frustrated coupling between the alternating spin chains. We deduce the minimal model containing such a frustration, and show that it gives an excellent account of the magnon dispersion, static susceptibility and electron spin resonance absorption. We consider two-magnon states which bind due to frustration, and demonstrate that these may provide a consistent explanation for the second mode.Comment: RevTeX, 5 pages, 6 figures, compressed from first versio

Excitation Spectra of Structurally Dimerized and Spin-Peierls Chains in a Magnetic Field

The dynamical spin structure factor and the Raman response are calculated for structurally dimerized and spin-Peierls chains in a magnetic field, using exact diagonalization techniques. In both cases there is a spin liquid phase composed of interacting singlet dimers at small fields h < h_c1, an incommensurate regime (h_c1 < h < h_c2) in which the modulation of the triplet excitation spectra adapts to the applied field, and a fully spin polarized phase above an upper critical field h_c2. For structurally dimerized chains, the spin gap closes in the incommensurate phase, whereas spin-Peierls chains remain gapped. In the spin liquid regimes, the dominant feature of the triplet spectra is a one-magnon bound state, separated from a continuum of states at higher energies. There are also indications of a singlet bound state above the one-magnon triplet.Comment: RevTex, 10 pages with 8 eps figure

Excitations in one-dimensional S=1/2 quantum antiferromagnets

The transition from dimerized to uniform phases is studied in terms of spectral weights for spin chains using continuous unitary transformations (CUTs). The spectral weights in the S=1 channel are computed perturbatively around the limit of strong dimerization. We find that the spectral weight is concentrated mainly in the subspaces with a small number of elementary triplets (triplons), even for vanishing dimerization. So, besides spinons, triplons may be used as elementary excitations in spin chains. We conclude that there is no necessity to use fractional excitations in low-dimensional, undoped or doped quantum antiferromagnets.Comment: 4 pages, 1 figure include

Phenomenological theory of spin excitations in La- and Y-based cuprates

Motivated by recent inelastic neutron scattering (INS) experiments on La-based cuprates and based on the fermiology theories, we study the spin susceptibility for La-based (e.g., La$_{2-x}$Sr$_x$CuO$_4$) and Y-based (e.g., YBa$_2$Cu$_3$O$_y$) cuprates, respectively. The spin excitation in YBa$_2$Cu$_3$O$_y$ is dominated by a sharp resonance peak at the frequency 40 meV in the superconducting state. Below and above the resonance frequency, the incommensurate (IC) peaks develop and the intensity of the peaks decreases dramatically. In the normal state, the resonant excitation does not occur and the IC peaks are merged into commensurate ones. The spin excitation of La$_{2-x}$Sr$_x$CuO$_4$ is significantly different from that of Y-based ones, namely, the resonance peak does not exist due to the decreasing of the superconducting gap and the presence of the possible spin-stripe order. The spectra are only enhanced at the expected resonance frequency (about 18 meV) while it is still incommensurate. On the other hand, another frequency scale at the frequency 55 meV is also revealed, namely the spectra are commensurate and local maximum at this frequency. We elaborate all the results based on the Fermi surface topology and the d-wave superconductivity, and suggest that the spin-stripe order be also important in determining the spin excitation of La-based cuprates. A coherent picture for the spin excitations is presented for Y-based and La-based cuprates.Comment: 8 pages, 8 figure

Vertex corrections in the dynamic structure factor in spin ladders

We combine the results of perturbative continuous unitary transformations with a mean-field calculation to determine the evolution of the single-mode, i.e., one-triplon, contribution to the dynamic structure factor of a two-leg $S=1/2$ ladder on increasing temperature from zero to a finite value. The temperature dependence is induced by two effects: (i) no triplon can be excited on a rung where a thermally activated triplon is present; (ii) conditional excitation processes take place if a thermally activated triplon is present. Both effects diminish the one-triplon spectral weight upon heating. It is shown that the second effect is the dominant vertex correction in the calculation of the dynamic structure factor. The matrix elements describing the conditional triplon excitation in the two-leg Heisenberg ladder with additional four-spin ring exchange are calculated perturbatively up to order 9. The calculated results are compared to those of an inelastic neutron scattering experiment on the cuprate-ladder compound La$_{4}$Sr$_{10}$Cu$_{24}$O$_{41}$ showing convincing agreement for established values of the exchange constants.Comment: 14 pages, 15 figure

Incompatibility of modulated checkerboard patterns with the neutron scattering resonance peak in cuprate superconductors

Checkerboard patterns have been proposed in order to explain STM experiments on the cuprates BSCCO and Na-CCOC. However the presence of these patterns has not been confirmed by a bulk probe such as neutron scattering. In particular, simple checkerboard patterns are inconsistent with neutron scattering data, in that they have low energy incommsensurate (IC) spin peaks rotated 45 degrees from the direction of the charge IC peaks. However, it is unclear whether other checkerboard patterns can solve the problem. In this paper, we have studied more complicated checkerboard patterns ("modulated checkerboards") by using spin wave theory and analyzed noncollinear checkerboards as well. We find that the high energy response of the modulated checkerboards is inconsistent with neutron scattering results, since they fail to exhibit a resonance peak at (pi,pi), which has recently been shown to be a universal feature of cuprate superconductors. We further argue that the newly proposed noncollinear checkerboard also lacks a resonance peak. We thus conclude that to date no checkerboard pattern has been proposed which satisfies both the low energy constraints and the high energy constraints imposed by the current body of experimental data in cuprate superconductors.Comment: 5 pages, 5 figures, Fig.2 update

Efficient Coherent Control by Optimized Sequences of Pulses of Finite Duration

Reliable long-time storage of arbitrary quantum states is a key element for quantum information processing. In order to dynamically decouple a spin or quantum bit from a dephasing environment, we introduce an optimized sequence of $N$ control pulses of finite durations \tau\pp and finite amplitudes. The properties of this sequence of length $T$ stem from a mathematically rigorous derivation. Corrections occur only in order $T^{N+1}$ and \tau\pp^3 without mixed terms such as T^N\tau\pp or T^N\tau\pp^2. Based on existing experiments, a concrete setup for the verification of the properties of the advocated realistic sequence is proposed.Comment: 8 pages, 1 figur