Generalization of short coherent control pulses: extension to arbitrary rotations

We generalize the problem of the coherent control of small quantum systems to the case where the quantum bit (qubit) is subject to a fully general rotation. Following the ideas developed in Pasini et al (2008 Phys. Rev. A 77, 032315), the systematic expansion in the shortness of the pulse is extended to the case where the pulse acts on the qubit as a general rotation around an axis of rotation varying in time. The leading and the next-leading corrections are computed. For certain pulses we prove that the general rotation does not improve on the simpler rotation with fixed axis.Comment: 6 pages, no figures; published versio

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

High Order Coherent Control Sequences of Finite-Width Pulses

The performance of sequences of designed pulses of finite length $\tau$ is analyzed for a bath of spins and it is compared with that of sequences of ideal, instantaneous pulses. The degree of the design of the pulse strongly affects the performance of the sequences. Non-equidistant, adapted sequences of pulses, which equal instantaneous ones up to $\mathcal{O}(\tau^3)$, outperform equidistant or concatenated sequences. Moreover, they do so at low energy cost which grows only logarithmically with the number of pulses, in contrast to standard pulses with linear growth.Comment: 6 pages, 5 figures, new figures, published versio

Electron spectra close to a metal-to-insulator transition

A high-resolution investigation of the electron spectra close to the metal-to-insulator transition in dynamic mean-field theory is presented. An all-numerical, consistent confirmation of a smooth transition at zero temperature is provided. In particular, the separation of energy scales is verified. Unexpectedly, sharp peaks at the inner Hubbard band edges occur in the metallic regime. They are signatures of the important interaction between single-particle excitations and collective modes.Comment: RevTeX 4, 4 pages, 4 eps figures; published versio

Conductivity in a symmetry broken phase: Spinless fermions with 1/d1/d corrections

The dynamic conductivity $\sigma(\omega)$ of strongly correlated electrons in a symmetry broken phase is investigated in the present work. The model considered consists of spinless fermions with repulsive interaction on a simple cubic lattice. The investigated symmetry broken phase is the charge density wave (CDW) with wave vector $Q=(\pi,\pi,\pi)^\dagger$ which occurs at half-filling. The calculations are based on the high dimensional approach, i.e. an expansion in the inverse dimension $1/d$ is used. The finite dimensionality is accounted for by the inclusion of linear terms in $1/d$ and the true finite dimensional DOS. Special care is paid to the setup of a conserving approximation in the sense of Baym/Kadanoff without inconsistencies. The resulting Bethe-Salpeter equation is solved for the dynamic conductivity in the non symmetry broken and in the symmetry broken phase (AB-CDW). The dc-conductivity is reduced drastically in the CDW. Yet it does not vanish in the limit $T \to 0$ due to a subtle cancellation of diverging mobility and vanishing DOS. In the dynamic conductivity $\sigma(\omega)$ the energy gap induced by the symmetry breaking is clearly discernible. In addition, the vertex corrections of order $1/d$ lead to an excitonic resonance lying within the gap.Comment: 23 pages, 19 figures included with psfig, Revtex; Physical Review B15, in press (October/November 1996) depending on the printer/screen driver, it might be necessary to comment out figures 3,4,5,10,11,12,19 and have them printed separatel

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

Unifying Magnons and Triplons in Stripe-Ordered Cuprate Superconductors

Based on a two-dimensional model of coupled two-leg spin ladders, we derive a unified picture of recent neutron scattering data of stripe-ordered La_(15/8)Ba_(1/8)CuO_4, namely of the low-energy magnons around the superstructure satellites and of the triplon excitations at higher energies. The resonance peak at the antiferromagnetic wave vector Q_AF in the stripe-ordered phase corresponds to a saddle point in the dispersion of the magnetic excitations. Quantitative agreement with the neutron data is obtained for J= 130-160 meV and J_cyc/J = 0.2-0.25.Comment: 4 pages, 4 figures included updated version taking new data into account; factor in spectral weight corrected; Figs. 2 and 4 change