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

Doping dependence of spin excitations in the stripe phase of high-Tc superconductors

Based on the time-dependent Gutzwiller approximation for the extended Hubbard model we calculate the energy and momentum dependence of spin excitations for striped ground states. Our starting point correctly reproduces the observed doping dependence of the incommensurability in La-based cuprates and the dispersion of magnetic modes in the insulating parent compound. This allows us to make quantitative predictions for the doping evolution of the dispersion of magnetic modes in the stripe phase including the energy and intensity of the resonance peak as well as the velocity of the spin-wave like Goldstone mode. In the underdoped regime $n_h<1/8$ we find a weak linear dependence of $\omega_{res}$ on doping whereas the resonance energy significantly shifts to higher values when the charge concentration in the stripes starts to deviate from half-filling for $n_h>1/8$. The velocity $c$ is non-monotonous with a minimum at 1/8 in coincidence with a well known anomaly in $T_c$. Our calculations are in good agreement with available experimental data. We also compare our results with analogous computations based on linear spin-wave theory.Comment: 18 pages, 14 figures, revised and extended 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

Spin Waves in Quantum Antiferromagnets

Using a self-consistent mean-field theory for the $S=1/2$ Heisenberg antiferromagnet Kr\"uger and Schuck recently derived an analytic expression for the dispersion. It is exact in one dimension ($d=1$) and agrees well with numerical results in $d=2$. With an expansion in powers of the inverse coordination number $1/Z$ ($Z=2d$) we investigate if this expression can be {\em exact} for all $d$. The projection method of Mori-Zwanzig is used for the {\em dynamical} spin susceptibility. We find that the expression of Kr\"uger and Schuck deviates in order $1/Z^2$ from our rigorous result. Our method is generalised to arbitrary spin $S$ and to models with easy-axis anisotropy \D. It can be systematically improved to higher orders in $1/Z$. We clarify its relation to the $1/S$ expansion.Comment: 8 pages, uuencoded compressed PS-file, accepted as Euro. Phys. Lette

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

Spectral weight contributions of many-particle bound states and continuum

Cluster expansion methods are developed for calculating the spectral weight contributions of multiparticle excitations - continuum and bound states - to high orders. A complete 11th order calculation is carried out for the alternating Heisenberg chain. For $\lambda=0.27$, relevant to the material $Cu(NO_3)_2.2.5D_2O$, we present detailed spectral weights for the two-triplet continuum and all bound states. We also examine variation of the relative weights of one and two-particle states with bond alternation from the dimerized to the uniform chain limit.Comment: 4 pages, 5 figures, revte

Fractional and Integer Excitations in Quantum Antiferromagnetic Spin 1/2 Ladders

Spectral densities are computed in unprecedented detail for quantum antiferromagnetic spin 1/2 two-leg ladders. These results were obtained due to a major methodical advance achieved by optimally chosen unitary transformations. The approach is based on dressed integer excitations. Considerable weight is found at high energies in the two-particle sector. Precursors of fractional spinon physics occur implying that there is no necessity to resort to fractional excitations in order to describe features at higher energies.Comment: 6 pages, 4 figures included, minor text changes, improved figure

Universal dynamical decoupling of a single solid-state spin from a spin bath

Controlling the interaction of a single quantum system with its environment is a fundamental challenge in quantum science and technology. We dramatically suppress the coupling of a single spin in diamond with the surrounding spin bath by using double-axis dynamical decoupling. The coherence is preserved for arbitrary quantum states, as verified by quantum process tomography. The resulting coherence time enhancement is found to follow a general scaling with the number of decoupling pulses. No limit is observed for the decoupling action up to 136 pulses, for which the coherence time is enhanced more than 25 times compared to spin echo. These results uncover a new regime for experimental quantum science and allow to overcome a major hurdle for implementing quantum information protocols.Comment: submitted 24 May 2010; published online 9 September 201

Magnetic properties of (VO)_2P_2O_7: two-plane structure and spin-phonon interactions

Detailed experiments on single-crystal (VO)_2P_2O_7 continue to reveal new and unexpected features. We show that a model composed of two, independent planes of spin chains with frustrated magnetic coupling is consistent with nuclear magnetic resonance and inelastic neutron scattering measurements. The pivotal role of PO_4 groups in mediating intrachain exchange interactions explains both the presence of two chain types and their extreme sensitivity to certain lattice vibrations, which results in the strong magnetoelastic coupling observed by light scattering. We compute the respective modifications of the spin and phonon dynamics due to this coupling, and illustrate their observable consequences on the phonon frequencies, magnon dispersions, static susceptibility and specific heat.Comment: 10 pages, 9 figure

Exchange-Only Dynamical Decoupling in the 3-Qubit Decoherence Free Subsystem

The Uhrig dynamical decoupling sequence achieves high-order decoupling of a single system qubit from its dephasing bath through the use of bang-bang Pauli pulses at appropriately timed intervals. High-order decoupling of single and multiple qubit systems from baths causing both dephasing and relaxation can also be achieved through the nested application of Uhrig sequences, again using single-qubit Pauli pulses. For the 3-qubit decoherence free subsystem (DFS) and related subsystem encodings, Pauli pulses are not naturally available operations; instead, exchange interactions provide all required encoded operations. Here we demonstrate that exchange interactions alone can achieve high-order decoupling against general noise in the 3-qubit DFS. We present decoupling sequences for a 3-qubit DFS coupled to classical and quantum baths and evaluate the performance of the sequences through numerical simulations