K. A. Valiev

Schmidt modes and entanglement in continuous-variable quantum systems

The extraction of Schmidt modes for continuous-variable systems is considered. An algorithm based on the singular-value decomposition of a matrix is proposed. It is applied to the entanglement in (i) an atom—photon system with spontaneous emission and (ii) a system of biphotons with spontaneous parametric downconversion (SPDC) of type II. For the atom—photon system, the evolution of entangled states is found to be governed by a parameter approximately equal to the fine-structure constant times the atom-to-electron mass ratio. An analysis is made of the dynamics of atom—photon entanglement on the assumption that the system’s evolution is determined by the superposition of an initial and a final state. It is shown that in the course of emission the entanglement entropy first rises on a timescale of order the excited-state lifetime and then falls, approaching asymptotically a residual level due to the initial energy spread of the atomic packet (momentum spread squared). SPDC of type II is analyzed by means of the polarization density matrix and a newly introduced coherence parameter for two spatially separated modes. The loss of intermodal coherence is addressed that results from the difference in behavior between ordinary-and extraordinary-ray photons in a nonlinear crystal. The degree of intermodal coherence is investigated as a function of the product of crystal length and pump bandwidth.

Nano- and micrometer-scale thin-film-interconnection failure theory and simulation and metallization lifetime prediction, Part 1: A general theory of vacancy transport, mechanical-stress generation, and void nucleation under electromigration in relation to multilevel-metallization degeneration and failure

The physical principles are considered of on-chip interconnection degeneration and failure in sub-1-µm technologies from the viewpoint of multilevel-metallization reliability. A general theory and simulation results are presented that deal with electromigration-induced failure of thin-film conducting tracks on the micro- and nanometer scales. They provide a detailed treatment of micro-, meso-, and nanoscopic mechanisms underlying the deformation and breaking of actual interconnection configurations. Parts 1 and 2 contain (i) the derivation and analysis of basic kinetic equations; (ii) the formulation and solution of three-dimensional boundary-value problems representing the transport of vacancies (both in the bulk and along grain boundaries) and the development of deformation and stress; (iii) models of void nucleation and development; (iv) an analysis of a multilevel-metallization lifetime; and (v) the identification of potential break locations in a multilevel metallization in relation to current density, metallization structure and layout, temperature, and the grain structure of the conducting material. Part 3 deals with electromigration in doped on-chip polycrystalline interconnections in terms of lengthening their lifetime. To predict electromigration resistance, models are constructed that represent the influence of texture and other grain-boundary properties on the effective charges of native and dopant ions.

Quantum computers: Achievements, implementation difficulties, and prospects

A review of the principles of operation of quantum computers and their elements is presented. The radical advantage of quantum algorithms for processing information over the classical ones is discussed, quantum entanglement is considered as the basic resource of quantum computations, and the most promising and interesting proposals on realization of quantum computers on the basis of trapped ions, nuclear spins, quantum dots, superconducting structures, and others are described. This review reflects the materials of the report presented at the scientific session of the Department of Nanotechnologies and Information Technologies of the Russian Academy of Sciences on February 25, 2010.

A Microwave High-Density Plasma Source for Submicron Silicon IC Technology

A microwave high-density plasma source is applied for room-temperature deposition of thin SiO2films, filling of submicron trenches, local planarization of the chip surface, etching of deep trenches in the insulator, and resist stripping after ion implantation. The structures obtained meet stringent demands for current technologies. Uniform processing of wafers up to 300 mm in diameter is demonstrated.

Nano- and micrometer-scale thin-film-interconnection failure theory and simulation and metallization lifetime prediction, Part 2: Polycrystalline-line degradation and bulk failure

The degradation and bulk failure of a polycrystalline interconnect line caused by vacancy electromigration along grain boundaries and vacancy-cluster nucleation at triple points in the bulk conductor are investigated within the general theory of the electromigration-induced degradation and failure of thin-film on-chip interconnect lines, presented in Part 1 [1]. The general equations are tailored to deal with vacancy electromigration, mechanical-stress generation, and void nucleation at triple points. Appropriate boundaryvalue problems are formulated, and numerical methods and procedures to solve them are developed and implemented in software. Computer simulations are performed to identify a pattern of electromigration failure at triple points. On this basis, (1) interconnect lifetime is investigated over wide ranges of variation of material, structural, geometric, and operating parameters, and (2) the current-density and temperature dependence—of the mechanical stress, vacancy concentration, and level of vacancy supersaturation at a triple point, and of void radius and time to nucleation-is examined and explained. The simulation results are found to agree well with previous experiments. This investigation could be seen as a natural continuation of our study of electromigration failures developed by multilevel-metallization systems as a result of interconnect failure near via junctions or at open ends [1]. Together they cover most mechanisms of electromigration failure suffered by metallization systems.

Perfectly and imperfectly controlled quantum operations on a charge qubit

A theoretical investigation is presented into the coherent dynamics of a charge qubit in the form of two tunnel-coupled quantum dots containing a single electron, with the logic states represented by electron orbitals localized at the quantum dots. Analytical expressions are derived for the evolution of a one-or two-qubit system in an applied field. The system and field parameters are evaluated in terms of performing basic one-qubit operations. The possibility is explored for implementing the CNOT operation in a two-qubit system driven by error-free or error-prone control pulses.

Information aspects of “which-path” interference experiments with microparticles

The Schmidt expansion method is used to consider the informational aspects of the problem concerned with monitoring the process of interference of quantum particles. The far-field diffraction pattern specified by the probability density of the distribution of the particle momentum is represented as a mixture of densities of the corresponding Schmidt modes, whose number coincides with the number of slits in the screen. The optical coherence is described on the basis of the procedure of complementation of the mixture to a pure state. Information characteristics are introduced to describe the quality of the interference pattern. The relationship between the visibility of the interference pattern and the Schmidt number is found and examined. Different “which-path” experiments are analyzed. The results of numerical simulation of interference at two and three slits for Rydberg atoms, whose path passes through resonators capable of providing data on the trajectory of the atom, are described.

Multiparticle entangled quantum states and modeling of thermodynamic statistical distributions

Thermodynamic equilibrium of a system is considered as a consequence of quantum entanglement of the vacuum state of the system. An explicit mathematical model of multiparticle entangled pure quantum states is developed and analyzed. Within the framework of this model, the measurement process gives rise to probability distributions that exactly correspond to thermal equilibrium of the system in a thermostat.