179 research outputs found
Accurate Transfer Maps for Realistic Beamline Elements: Part I, Straight Elements
The behavior of orbits in charged-particle beam transport systems, including
both linear and circular accelerators as well as final focus sections and
spectrometers, can depend sensitively on nonlinear fringe-field and
high-order-multipole effects in the various beam-line elements. The inclusion
of these effects requires a detailed and realistic model of the interior and
fringe fields, including their high spatial derivatives. A collection of
surface fitting methods has been developed for extracting this information
accurately from 3-dimensional field data on a grid, as provided by various
3-dimensional finite-element field codes. Based on these realistic field
models, Lie or other methods may be used to compute accurate design orbits and
accurate transfer maps about these orbits. Part I of this work presents a
treatment of straight-axis magnetic elements, while Part II will treat bending
dipoles with large sagitta. An exactly-soluble but numerically challenging
model field is used to provide a rigorous collection of performance benchmarks.Comment: Accepted to PRST-AB. Changes: minor figure modifications, reference
added, typos corrected
Solvable Map Representation Of A Nonlinear Symplectic Map
The evolution of a particle under the action of a beam transport system can be represented by a nonlinear symplectic map M. This map can be factorized into a product of Lie transformations. The evaluation of any given lie transformation in general requires the summation of an infinite number of terms. There are several ways of dealing with this difficulty: The summation can be truncated, thus producing a map that is nonsymplectic, but still useful for short term tracking. Alternatively, for long term tracking, the Lie transformation can be replaced by some symplectic map that agrees with it to some order and can be evaluated exactly. This paper shows how this may be done using solvable symplectic maps. A solvable map gives rise to a power series that either terminates or can be summed explicitly. This method appears to work quite well in the various examples that we have considered
The Moyal-Lie Theory of Phase Space Quantum Mechanics
A Lie algebraic approach to the unitary transformations in Weyl quantization
is discussed. This approach, being formally equivalent to the
-quantization, is an extension of the classical Poisson-Lie formalism
which can be used as an efficient tool in the quantum phase space
transformation theory.Comment: 15 pages, no figures, to appear in J. Phys. A (2001
Quantum logic gates for coupled superconducting phase qubits
Based on a quantum analysis of two capacitively coupled current-biased
Josephson junctions, we propose two fundamental two-qubit quantum logic gates.
Each of these gates, when supplemented by single-qubit operations, is
sufficient for universal quantum computation. Numerical solutions of the
time-dependent Schroedinger equation demonstrate that these operations can be
performed with good fidelity.Comment: 4 pages, 5 figures, revised for publicatio
Comparison of coherence times in three dc SQUID phase qubits
We report measurements of spectroscopic linewidth and Rabi oscillations in
three thin-film dc SQUID phase qubits. One device had a single-turn Al loop,
the second had a 6-turn Nb loop, and the third was a first order gradiometer
formed from 6-turn wound and counter-wound Nb coils to provide isolation from
spatially uniform flux noise. In the 6 - 7.2 GHz range, the spectroscopic
coherence times for the gradiometer varied from 4 ns to 8 ns, about the same as
for the other devices (4 to 10 ns). The time constant for decay of Rabi
oscillations was significantly longer in the single-turn Al device (20 to 30
ns) than either of the Nb devices (10 to 15 ns). These results imply that
spatially uniform flux noise is not the main source of decoherence or
inhomogenous broadening in these devices.Comment: 4 pages, 5 figures, accepted for publication in IEEE Trans. Appl.
Supercon
Snell's Law from an Elementary Particle Viewpoint
Snell's law of light deflection between media with different indices of
refraction is usually discussed in terms of the Maxwell electromagnetic wave
theory. Snell's law may also be derived from a photon beam theory of light
rays. This latter particle physics view is by far the most simple one for
understanding the laws of refraction.Comment: ReVTeX Format 2 *.eps figure
Strong-field effects in the Rabi oscillations of the superconducting phase qubit
Rabi oscillations have been observed in many superconducting devices, and
represent prototypical logic operations for quantum bits (qubits) in a quantum
computer. We use a three-level multiphoton analysis to understand the behavior
of the superconducting phase qubit (current-biased Josephson junction) at high
microwave drive power. Analytical and numerical results for the ac Stark shift,
single-photon Rabi frequency, and two-photon Rabi frequency are compared to
measurements made on a dc SQUID phase qubit with Nb/AlOx/Nb tunnel junctions.
Good agreement is found between theory and experiment.Comment: 4 pages, 4 figures, accepted for publication in IEEE Trans. Appl.
Supercon
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