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Search Results: 1 - 10 of 303159 matches for " Alex J. Dragt "
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A Lie connection between Hamiltonian and Lagrangian optics
Alex J. Dragt
Discrete Mathematics & Theoretical Computer Science , 1997,
Abstract: It is shown that there is a non-Hamiltonian vector field that provides a Lie algebraic connection between Hamiltonian and Lagrangian optics. With the aid of this connection, geometrical optics can be formulated in such a way that all aberrations are attributed to ray transformations occurring only at lens surfaces. That is, in this formulation there are no aberrations arising from simple transit in a uniform medium. The price to be paid for this formulation is that the Lie algebra of Hamiltonian vector fields must be enlarged to include certain non-Hamiltonian vector fields. It is shown that three such vector fields are required at the level of third-order aberrations, and sufficient machinery is developed to generalize these results to higher order.
How Wigner Functions Transform Under Symplectic Maps
Alex J. Dragt,Salman Habib
Physics , 1998,
Abstract: It is shown that, while Wigner and Liouville functions transform in an identical way under linear symplectic maps, in general they do not transform identically for nonlinear symplectic maps. Instead there are ``quantum corrections'' whose hbar tending to zero limit may be very complicated. Examples of the behavior of Wigner functions in this limit are given in order to examine to what extent the corresponding Liouville densities are recovered.
Accurate Transfer Maps for Realistic Beamline Elements: Part I, Straight Elements
Chad E. Mitchell,Alex J. Dragt
Physics , 2010, DOI: 10.1103/PhysRevSTAB.13.064001
Abstract: 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.
Poincare Analyticity and the Complete Variational Equations
Dobrin Kaltchev,Alex Dragt
Physics , 2011, DOI: 10.1016/j.physd.2012.08.010
Abstract: According to a theorem of Poincare, the solutions to differential equations are analytic functions of (and therefore have Taylor expansions in) the initial conditions and various parameters providing the right sides of the differential equations are analytic in the variables, the time, and the parameters. We describe how these Taylor expansions may be obtained, to any desired order, by integration of what we call the complete variational equations. As illustrated in a Duffing equation stroboscopic map example, these Taylor expansions, truncated at an appropriate order thereby providing polynomial approximations, can well reproduce the behavior (including infinite period doubling cascades and strange attractors) of the solutions of the underlying differential equations.
Convergence of Taylor Transfer Map for Duffing Equation
Dobrin Kaltchev,Alex Dragt
Physics , 2012,
Abstract: According to a theorem of Poincare, the solutions to differential equations are analytic functions of (and therefore have Taylor expansions in) the initial conditions and various parameters provided that the right sides of the differential equations are analytic in the variables, the time, and the parameters. These Taylor expansions, which provide a transfer map M between initial and final conditions, may be obtained, to any desired order, by integration of the complete variational equations. As an example of this approach, the convergence of such an expansion is investigated for the Duffing equation stroboscopic map in the vicinity of a infinite period doubling cascade and resulting strange attractor.
Quantum logic gates for coupled superconducting phase qubits
Frederick W. Strauch,Philip R. Johnson,Alex J. Dragt,C. J. Lobb,J. R. Anderson,F. C. Wellstood
Physics , 2003, DOI: 10.1103/PhysRevLett.91.167005
Abstract: 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.
Macroscopic tunnel splittings in superconducting phase qubits
Philip R. Johnson,William T. Parsons,Frederick W. Strauch,J. R. Anderson,Alex J. Dragt,C. J. Lobb,F. C. Wellstood
Physics , 2004, DOI: 10.1103/PhysRevLett.94.187004
Abstract: Prototype Josephson-junction based qubit coherence times are too short for quantum computing. Recent experiments probing superconducting phase qubits have revealed previously unseen fine splittings in the transition energy spectra. These splittings have been attributed to new microscopic degrees of freedom (microresonators), a previously unknown source of decoherence. We show that macroscopic resonant tunneling in the extremely asymmetric double well potential of the phase qubit can have observational consequences that are strikingly similar to the observed data.
Spectroscopy of capacitively coupled Josephson-junction qubits
Philip R. Johnson,Frederick W. Strauch,Alex J. Dragt,Roberto C. Ramos,C. J. Lobb,J. R. Anderson,F. C. Wellstood
Physics , 2002, DOI: 10.1103/PhysRevB.67.020509
Abstract: We show that two capacitively-coupled Josephson junctions, in the quantum limit, form a simple coupled qubit system with effective coupling controlled by the junction bias currents. We compute numerically the energy levels and wave functions for the system, and show how these may be tuned to make optimal qubits. The dependence of the energy levels on the parameters can be measured spectroscopically, providing an important experimental test for the presence of entangled multiqubit states in Josephson-junction based circuits.
Exploring Minimal Scenarios to Produce Transversely Bright Electron Beams Using the Eigen-Emittance Concept
Leanne D. Duffy,Kip A. Bishofberger,Bruce C. Carlsten,Alex Dragt,Quinn R. Marksteiner,Steven J. Russell,Robert D. Ryne,Nikolai A. Yampolsky
Physics , 2011, DOI: 10.1016/j.nima.2011.06.096
Abstract: Next generation hard X-ray free electron lasers require electron beams with low transverse emittance. One proposal to achieve these low emittances is to exploit the eigen-emittance values of the beam. The eigen-emittances are invariant under linear beam transport and equivalent to the emittances in an uncorrelated beam. If a correlated beam with two small eigen-emittances can be produced, removal of the correlations via appropriate optics will lead to two small emittance values, provided non-linear effects are not too large. We study how such a beam may be produced using minimal linear correlations. We find it is theoretically possible to produce such a beam, however it may be more difficult to realize in practice. We identify linear correlations that may lead to physically realizable emittance schemes and discuss promising future avenues.
Multilevel effects in the Rabi oscillations of a Josephson phase qubit
S. K. Dutta,Frederick W. Strauch,R. M. Lewis,Kaushik Mitra,Hanhee Paik,T. A. Palomaki,Eite Tiesinga,J. R. Anderson,Alex J. Dragt,C. J. Lobb,F. C. Wellstood
Physics , 2008, DOI: 10.1103/PhysRevB.78.104510
Abstract: We present Rabi oscillation measurements of a Nb/AlOx/Nb dc superconducting quantum interference device (SQUID) phase qubit with a 100 um^2 area junction acquired over a range of microwave drive power and frequency detuning. Given the slightly anharmonic level structure of the device, several excited states play an important role in the qubit dynamics, particularly at high power. To investigate the effects of these levels, multiphoton Rabi oscillations were monitored by measuring the tunneling escape rate of the device to the voltage state, which is particularly sensitive to excited state population. We compare the observed oscillation frequencies with a simplified model constructed from the full phase qubit Hamiltonian and also compare time-dependent escape rate measurements with a more complete density-matrix simulation. Good quantitative agreement is found between the data and simulations, allowing us to identify a shift in resonance (analogous to the ac Stark effect), a suppression of the Rabi frequency, and leakage to the higher excited states.
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