Low temperature spin diffusion in the one-dimensional quantum O(3)O(3) nonlinear σ\sigma-model

An effective, low temperature, classical model for spin transport in the one-dimensional, gapped, quantum $O(3)$ non-linear $\sigma$-model is developed. Its correlators are obtained by a mapping to a model solved earlier by Jepsen. We obtain universal functions for the ballistic-to-diffusive crossover and the value of the spin diffusion constant, and these are claimed to be exact at low temperatures. Implications for experiments on one-dimensional insulators with a spin gap are noted.Comment: 4 pages including 3 eps-figures, Revte

High Magnetic Field ESR in the Haldane Spin Chains NENP and NINO

We present electron spin resonance experiments in the one-dimensional antiferromagnetic S=1 spin chains NENP and NINO in pulsed magnetic fields up to 50T. The measured field dependence of the quantum energy gap for B||b is analyzed using the exact diagonalization method and the density matrix renormalization group method (DMRG). A staggered anisotropy term (-1)^i d(S_i^x S_i^z + S_i^z S_i^x) was considered for the first time in addition to a staggered field term (-1)^i S_i^x B_st. We show that the spin dynamics in high magnetic fields strongly depends on the orthorhombic anisotropy E.Comment: 4 pages, RevTeX, 4 figure

Effects of anisotropic spin-exchange interactions in spin ladders

We investigate the effects of the Dzialoshinskii-Moriya (DM) and Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) interactions on various thermodynamic and magnetic properties of a spin 1/2 ladder. Using the Majorana fermion representation, we derive the spectrum of low energy excitations for a pure DM interaction and in presence of a superimposed KSEA interaction. We calculate the various correlation functions for both cases and discuss how they are modified with respect to the case of an isotropic ladder. We also discuss the electron spin resonance (ESR) spectrum of the system and show that it is strongly influenced by the orientation of the magnetic field with respect to the Dzialoshinskii-Moriya vector. Implications of our calculations for NMR and ESR experiments on ladder systems are discussed.Comment: 14 pages, 4 eps figures, corrected calculation of NMR rate (v3

Identification of Nuclear Relaxation Processes in a Gapped Quantum Magnet: Proton NMR in the S=1/2 Heisenberg Ladder Cu2(C5H12N2)2Cl4

The proton hyperfine shift K and NMR relaxation rate $1/T_1$ have been measured as a function of temperature in the S=1/2 Heisenberg antiferromagnetic ladder Cu2(C5H12N2)2Cl4. The presence of a spin gap $\Delta \simeq J_\perp-J_\parallel$ in this strongly coupled ladder ($J_\parallel < J_\perp$) is supported by the K and $1/T_1$ results. By comparing $1/T_1$ at two different proton sites, we infer the evolution of the spectral functions $S_z(q,\omega_n)$ and $S_\perp(q,\omega_n)$. When the gap is significantly reduced by the magnetic field, two different channels of nuclear relaxation, specific to gapped antiferromagnets, are identified and are in agreement with theoretical predictions.Comment: 4 pages, 4 figures, to be published in Phys. Rev. Letter

Long-time Low-latency Quantum Memory by Dynamical Decoupling

Quantum memory is a central component for quantum information processing devices, and will be required to provide high-fidelity storage of arbitrary states, long storage times and small access latencies. Despite growing interest in applying physical-layer error-suppression strategies to boost fidelities, it has not previously been possible to meet such competing demands with a single approach. Here we use an experimentally validated theoretical framework to identify periodic repetition of a high-order dynamical decoupling sequence as a systematic strategy to meet these challenges. We provide analytic bounds-validated by numerical calculations-on the characteristics of the relevant control sequences and show that a "stroboscopic saturation" of coherence, or coherence plateau, can be engineered, even in the presence of experimental imperfection. This permits high-fidelity storage for times that can be exceptionally long, meaning that our device-independent results should prove instrumental in producing practically useful quantum technologies.Comment: abstract and authors list fixe

Modulating attentional load affects numerosity estimation: evidence against a pre-attentive subitizing mechanism

Traditionally, the visual enumeration of a small number of items (1 to about 4), referred to as subitizing, has been thought of as a parallel and pre-attentive process and functionally different from the serial attentive enumeration of larger numerosities. We tested this hypothesis by employing a dual task paradigm that systematically manipulated the attentional resources available to an enumeration task. Enumeration accuracy for small numerosities was severely decreased as more attentional resources were taken away from the numerical task, challenging the traditionally held notion of subitizing as a pre-attentive, capacity-independent process. Judgement of larger numerosities was also affected by dual task conditions and attentional load. These results challenge the proposal that small numerosities are enumerated by a mechanism separate from large numerosities and support the idea of a single, attention-demanding enumeration mechanism

Free Energy of an Inhomogeneous Superconductor: a Wave Function Approach

A new method for calculating the free energy of an inhomogeneous superconductor is presented. This method is based on the quasiclassical limit (or Andreev approximation) of the Bogoliubov-de Gennes (or wave function) formulation of the theory of weakly coupled superconductors. The method is applicable to any pure bulk superconductor described by a pair potential with arbitrary spatial dependence, in the presence of supercurrents and external magnetic field. We find that both the local density of states and the free energy density of an inhomogeneous superconductor can be expressed in terms of the diagonal resolvent of the corresponding Andreev Hamiltonian, resolvent which obeys the so-called Gelfand-Dikii equation. Also, the connection between the well known Eilenberger equation for the quasiclassical Green's function and the less known Gelfand-Dikii equation for the diagonal resolvent of the Andreev Hamiltonian is established. These results are used to construct a general algorithm for calculating the (gauge invariant) gradient expansion of the free energy density of an inhomogeneous superconductor at arbitrary temperatures.Comment: REVTeX, 28 page

Theory of Scanning Tunneling Spectroscopy of Magnetic-Field-Induced Discrete Nodal States in a D-Wave Superconductor

In the presence of an external magnetic field, the low lying elementary excitations of a d-wave superconductor have quantized energy and their momenta are locked near the node direction. It is argued that these discrete states can most likely be detected by a local probe, such as a scanning tunneling microscope. The low temperature local tunneling conductance on the Wigner-Seitz cell boundaries of the vortex lattice is predicted to show peaks spaced as $\pm \sqrt{n}, n ={0,1,2, ...}$. The $n=0$ peak is anomalous, and it is present only if the superconducting order parameter changes sign at certain points on the Fermi surface. Away from the cell boundary, where the superfluid velocity is nonzero, each peak splits, in general, into four peaks, corresponding to the number of nodes in the order parameter.Comment: RevTeX 3.0, 4 pages, 3 figures (included

Haldane-Gapped Spin Chains as Luttinger Liquids: Correlation Functions at Finite Field

We study the behavior of Heisenberg, antiferromagnetic, integer-spin chains in the presence of a magnetic field exceeding the attendant spin gap. For temperatures much smaller than the gap, the spin chains exhibit Luttinger liquid behavior. We compute exactly both the corresponding Luttinger parameter and the Fermi velocity as a function of magnetic field. This enables the computation of a number of correlators from which we derive the spin conductance, the expected form of the dynamic structure factor relevant to inelastic neutron scattering experiments, and NMR relaxation rates. We also comment upon the robustness of the magnetically induced gapless phase both to finite temperature and finite couplings between neighbouring chains.Comment: 32 pages, 8 figures; published version includes additions discussing the robustness of the magnetically induced gapless phase to ordering between chains as well as the relationship between the spin-1 chains and spin-1/2 ladders in the presence of a magnetic fiel

Decoherence-protected quantum gates for a hybrid solid-state spin register

Protecting the dynamics of coupled quantum systems from decoherence by the environment is a key challenge for solid-state quantum information processing. An idle qubit can be efficiently insulated from the outside world via dynamical decoupling, as has recently been demonstrated for individual solid-state qubits. However, protection of qubit coherence during a multi-qubit gate poses a non-trivial problem: in general the decoupling disrupts the inter-qubit dynamics, and hence conflicts with gate operation. This problem is particularly salient for hybrid systems, wherein different types of qubits evolve and decohere at vastly different rates. Here we present the integration of dynamical decoupling into quantum gates for a paradigmatic hybrid system, the electron-nuclear spin register. Our design harnesses the internal resonance in the coupled-spin system to resolve the conflict between gate operation and decoupling. We experimentally demonstrate these gates on a two-qubit register in diamond operating at room temperature. Quantum tomography reveals that the qubits involved in the gate operation are protected as accurately as idle qubits. We further illustrate the power of our design by executing Grover's quantum search algorithm, achieving fidelities above 90% even though the execution time exceeds the electron spin dephasing time by two orders of magnitude. Our results directly enable decoherence-protected interface gates between different types of promising solid-state qubits. Ultimately, quantum gates with integrated decoupling may enable reaching the accuracy threshold for fault-tolerant quantum information processing with solid-state devices.Comment: This is original submitted version of the paper. The revised and finalized version is in print, and is subjected to the embargo and other editorial restrictions of the Nature journa