Dynamical Stability and Quantum Chaos of Ions in a Linear Trap

The realization of a paradigm chaotic system, namely the harmonically driven oscillator, in the quantum domain using cold trapped ions driven by lasers is theoretically investigated. The simplest characteristics of regular and chaotic dynamics are calculated. The possibilities of experimental realization are discussed.Comment: 24 pages, 17 figures, submitted to Phys. Rev

The distribution of Transverse Aeolian Ridges on Mars

Abstract not available

Influence of qubit displacements on quantum logic operations in a silicon-based quantum computer with constant interaction

The errors caused by qubit displacements from their prescribed locations in an ensemble of spin chains are estimated analytically and calculated numerically for a quantum computer based on phosphorus donors in silicon. We show that it is possible to polarize (initialize) the nuclear spins even with displaced qubits by using Controlled NOT gates between the electron and nuclear spins of the same phosphorus atom. However, a Controlled NOT gate between the displaced electron spins is implemented with large error because of the exponential dependence of exchange interaction constant on the distance between the qubits. If quantum computation is implemented on an ensemble of many spin chains, the errors can be small if the number of chains with displaced qubits is small

Dynamical Stability of an Ion in a Linear Trap as a Solid-State Problem of Electron Localization

When an ion confined in a linear ion trap interacts with a coherent laser field, the internal degrees of freedom, related to the electron transitions, couple to the vibrational degree of freedom of the ion. As a result of this interaction, quantum dynamics of the vibrational degree of freedom becomes complicated, and in some ranges of parameters even chaotic. We analyze the vibrational ion dynamics using a formal analogy with the solid-state problem of electron localization. In particular, we show how the resonant approximation used in analysis of the ion dynamics, leads to a transition from a two-dimensional (2D) to a one-dimensional problem (1D) of electron localization. The localization length in the solid-state problem is estimated in cases of weak and strong interaction between the cites of the 2D cell by using the methods of resonance perturbation theory, common in analysis of 1D time-dependent dynamical systems.Comment: 18 pages RevTe

Dynamical fidelity of a solid-state quantum computation

In this paper we analyze the dynamics in a spin-model of quantum computer. Main attention is paid to the dynamical fidelity (associated with dynamical errors) of an algorithm that allows to create an entangled state for remote qubits. We show that in the regime of selective resonant excitations of qubits there is no any danger of quantum chaos. Moreover, in this regime a modified perturbation theory gives an adequate description of the dynamics of the system. Our approach allows to explicitly describe all peculiarities of the evolution of the system under time-dependent pulses corresponding to a quantum protocol. Specifically, we analyze, both analytically and numerically, how the fidelity decreases in dependence on the model parameters.Comment: 9 pages, 6 figures, submitted to PR

Double-Slit Interferometry with a Bose-Einstein Condensate

A Bose-Einstein "double-slit" interferometer has been recently realized experimentally by (Y. Shin et. al., Phys. Rev. Lett. 92 50405 (2004)). We analyze the interferometric steps by solving numerically the time-dependent Gross-Pitaevski equation in three-dimensional space. We focus on the adiabaticity time scales of the problem and on the creation of spurious collective excitations as a possible source of the strong dephasing observed experimentally. The role of quantum fluctuations is discussed.Comment: 4 pages, 3 figure

Radiative Tail in πe2\pi_{e2} Decay and Some Comments on μ−e\mu-e Universality

The result of lowest-order perturbation theory calculations of the photon and positron spectra in radiative pion(e2) decay are generalized to all orders of perturbation theory using the structure-function method. An additional source of radiative corrections to the ratio of the positron and muon channels of pion decay, due to emission of virtual and real photons and pairs, is considered. It depends on details of the detection of the final particles and is large enough to be taken into account in theoretical estimates with a level of accuracy of 0.1%.Comment: 5 pages, LaTeX, some misprints are corrected, submitted to Pisma Zh. Eksp. Teor. Fi

Graphene-based one-dimensional photonic crystal

A novel type of one-dimensional (1D) photonic crystal formed by the array of periodically located stacks of alternating graphene and dielectric stripes embedded into a background dielectric medium is proposed. The wave equation for the electromagnetic wave propagating in such structure solved in the framework of the Kronig-Penney model. The frequency band structure of 1D graphene-based photonic crystal is obtained analytically as a function of the filling factor and the thickness of the dielectric between graphene stripes. The photonic frequency corresponding to the electromagnetic wave localized by the defect of photonic crystal formed by the extra dielectric placed on the place of the stack of alternating graphene and dielectric stripes is obtained.Comment: 8 pages, 2 figure