The theory of heating of the quantum ground state of trapped ions

Using a displacement operator formalism, I analyse the depopulation of the vibrational ground state of trapped ions. Two heating times, one characterizing short time behaviour, the other long time behaviour are found. The short time behaviour is analyzed both for single and multiple ions, and a formula for the relative heating rates of different modes is derived. The possibility of correction of heating via the quantum Zeno effect, and the exploitation of the suppression of heating of higher modes to reduce errors in quantum computation is considered.Comment: 9 pages, 2 figure

Nonlinear coupling of continuous variables at the single quantum level

We experimentally investigate nonlinear couplings between vibrational modes of strings of cold ions stored in linear ion traps. The nonlinearity is caused by the ions' Coulomb interaction and gives rise to a Kerr-type interaction Hamiltonian H = n_r*n_s, where n_r,n_s are phonon number operators of two interacting vibrational modes. We precisely measure the resulting oscillation frequency shift and observe a collapse and revival of the contrast in a Ramsey experiment. Implications for ion trap experiments aiming at high-fidelity quantum gate operations are discussed

Transport in Transitory, Three-Dimensional, Liouville Flows

We derive an action-flux formula to compute the volumes of lobes quantifying transport between past- and future-invariant Lagrangian coherent structures of n-dimensional, transitory, globally Liouville flows. A transitory system is one that is nonautonomous only on a compact time interval. This method requires relatively little Lagrangian information about the codimension-one surfaces bounding the lobes, relying only on the generalized actions of loops on the lobe boundaries. These are easily computed since the vector fields are autonomous before and after the time-dependent transition. Two examples in three-dimensions are studied: a transitory ABC flow and a model of a microdroplet moving through a microfluidic channel mixer. In both cases the action-flux computations of transport are compared to those obtained using Monte Carlo methods.Comment: 30 pages, 16 figures, 1 table, submitted to SIAM J. Appl. Dyn. Sy

A scalable, high-speed measurement-based quantum computer using trapped ions

We describe a scalable, high-speed, and robust architecture for measurement-based quantum-computing with trapped ions. Measurement-based architectures offer a way to speed-up operation of a quantum computer significantly by parallelizing the slow entangling operations and transferring the speed requirement to fast measurement of qubits. We show that a 3D cluster state suitable for fault-tolerant measurement-based quantum computing can be implemented on a 2D array of ion traps. We propose the projective measurement of ions via multi-photon photoionization for nanosecond operation and discuss the viability of such a scheme for Ca ions.Comment: 4 pages, 3 figure

Multivariate Fitting and the Error Matrix in Global Analysis of Data

When a large body of data from diverse experiments is analyzed using a theoretical model with many parameters, the standard error matrix method and the general tools for evaluating errors may become inadequate. We present an iterative method that significantly improves the reliability of the error matrix calculation. To obtain even better estimates of the uncertainties on predictions of physical observables, we also present a Lagrange multiplier method that explores the entire parameter space and avoids the linear approximations assumed in conventional error propagation calculations. These methods are illustrated by an example from the global analysis of parton distribution functions.Comment: 13 pages, 5 figures, Latex; minor clarifications, fortran program made available; Normalization of Hessian matrix changed to HEP standar

Atmospheric Pco2 Perturbations Associated with the Central Atlantic Magmatic Province

The effects of a large igneous province on the concentration of atmospheric carbon dioxide (Pco2) are mostly unknown. In this study, we estimate Pco2 from stable isotopic values of pedogenic carbonates interbedded with volcanics of the Central Atlantic Magmatic Province (CAMP) in the Newark Basin, eastern North America. We find pre-CAMP Pco2 values of ~2000 parts per million (ppm), increasing to ~4400 ppm immediately after the first volcanic unit, followed by a steady decrease toward pre-eruptive levels over the subsequent 300 thousand years, a pattern that is repeated after the second and third flow units. We interpret each Pco2 increase as a direct response to magmatic activity (primary outgassing or contact metamorphism). The systematic decreases in Pco2 after each magmatic episode probably reflect consumption of atmospheric CO2 by weathering of silicates, stimulated by fresh CAMP volcanics

Sign of the crossed conductances at a FSF double interface

Crossed conductance in hybrid Ferromagnet / Superconductor / Ferromagnet (FSF) structures results from the competition between normal transmission and Andreev reflection channels. Crossed Andreev reflection (CAR) and elastic cotunneling (EC) between the ferromagnets are dressed by local Andreev reflections, which play an important role for transparent enough interfaces and intermediate spin polarizations. This modifies the simple result previously obtained at lowest order, and can explain the sign of the crossed resistances in a recent experiment [D. Beckmann {\sl et al.}, cond-mat/0404360]. This holds both in the multiterminal hybrid structure model (where phase averaging over the Fermi oscillations is introduced ``by hand'' within the approximation of a single non local process) and for infinite planar interfaces (where phase averaging naturally results in the microscopic solution with multiple non local processes).Comment: 9 pages, 7 figure

Paramagnetic Meissner effect in superconductors from self-consistent solutions of Ginzburg-Landau equations

The paramagnetic Meissner effect (PME) is observed in small superconducting samples, and a number of controversial explanations of this effect are proposed, but there is as yet no clear understanding of its nature. In the present paper PME is considered on the base of the Ginzburg-Landau theory (GL). The one-dimensional solutions are obtained in a model case of a long superconducting cylinder for different cylinder radii R, the GL-parameters \kappa and vorticities m. Acording to GL-theory, PME is caused by the presence of vortices inside the sample. The superconducting current flows around the vortex to screeen the vortex own field from the bulk of the sample. Another current flows at the boundary to screen the external field H from entering the sample. These screening currents flow in opposite directions and contribute with opposite signs to the total magnetic moment (or magnetization) of the sample. Depending on H, the total magnetization M may be either negative (diamagnetism), or positive (paramagnetism). A very complicated saw-like dependence M(H) (and other characteristics), which are obtained on the base of self-consistent solutions of the GL-equations, are discussed.Comment: 6 pages, 5 figures, RevTex, submitted to Phys. Rev.

Effective Hamiltonian Theory and Its Applications in Quantum Information

This paper presents a useful compact formula for deriving an effective Hamiltonian describing the time-averaged dynamics of detuned quantum systems. The formalism also works for ensemble-averaged dynamics of stochastic systems. To illustrate the technique we give examples involving Raman processes, Bloch-Siegert shifts and Quantum Logic Gates.Comment: 5 pages, 3 figures, to be published in Canadian Journal of Physic