14,952 research outputs found
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
Creation of entanglement in a scalable spin quantum computer with long-range dipole-dipole interaction between qubits
Creation of entanglement is considered theoretically and numerically in an
ensemble of spin chains with dipole-dipole interaction between the spins. The
unwanted effect of the long-range dipole interaction is compensated by the
optimal choice of the parameters of radio-frequency pulses implementing the
protocol. The errors caused by (i) the influence of the environment,(ii)
non-selective excitations, (iii) influence of different spin chains on each
other, (iv) displacements of qubits from their perfect locations, and (v)
fluctuations of the external magnetic field are estimated analytically and
calculated numerically. For the perfectly entangled state the z component, M,
of the magnetization of the whole system is equal to zero. The errors lead to a
finite value of M. If the number of qubits in the system is large, M can be
detected experimentally. Using the fact that M depends differently on the
parameters of the system for each kind of error, varying these parameters would
allow one to experimentally determine the most significant source of errors and
to optimize correspondingly the quantum computer design in order to decrease
the errors and M. Using our approach one can benchmark the quantum computer,
decrease the errors, and prepare the quantum computer for implementation of
more complex quantum algorithms.Comment: 31 page
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
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
Survival of quantum effects for observables after decoherence
When a quantum nonlinear system is linearly coupled to an infinite bath of
harmonic oscillators, quantum coherence of the system is lost on a decoherence
time-scale . Nevertheless, quantum effects for observables may still
survive environment-induced decoherence, and be observed for times much larger
than the decoherence time-scale. In particular, we show that the Ehrenfest
time, which characterizes a departure of quantum dynamics for observables from
the corresponding classical dynamics, can be observed for a quasi-classical
nonlinear oscillator for times . We discuss this observation in
relation to recent experiments on quantum nonlinear systems in the
quasi-classical region of parameters.Comment: submitted to PR
Orthogonality relations for triple modes at dielectric boundary surfaces
We work out the orthogonality relations for the set of Carniglia-Mandel
triple modes which provide a set of normal modes for the source-free
electromagnetic field in a background consisting of a passive dielectric
half-space and the vacuum, respectively. Due to the inherent computational
complexity of the problem, an efficient strategy to accomplish this task is
desirable, which is presented in the paper. Furthermore, we provide all main
steps for the various proofs pertaining to different combinations of triple
modes in the orthogonality integral.Comment: 15 page
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
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Abstract not available
Fluctuating Fronts as Correlated Extreme Value Problems: An Example of Gaussian Statistics
In this paper, we view fluctuating fronts made of particles on a
one-dimensional lattice as an extreme value problem. The idea is to denote the
configuration for a single front realization at time by the set of
co-ordinates of the
constituent particles, where is the total number of particles in that
realization at time . When are arranged in the ascending order
of magnitudes, the instantaneous front position can be denoted by the location
of the rightmost particle, i.e., by the extremal value
. Due to interparticle
interactions, at two different times for a single front
realization are naturally not independent of each other, and thus the
probability distribution [based on an ensemble of such front
realizations] describes extreme value statistics for a set of correlated random
variables. In view of the fact that exact results for correlated extreme value
statistics are rather rare, here we show that for a fermionic front model in a
reaction-diffusion system, is Gaussian. In a bosonic front model
however, we observe small deviations from the Gaussian.Comment: 6 pages, 3 figures, miniscule changes on the previous version, to
appear in Phys. Rev.
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