13 research outputs found
Engineering Entanglement: The Fast-Approach Phase Gate
Optimal-control techniques and a fast-approach scheme are used to implement a
collisional control phase gate in a model of cold atoms in an optical lattice,
significantly reducing the gate time as compared to adiabatic evolution while
maintaining high fidelity. New objective functionals are given for which
optimal paths are obtained for evolution that yields a control-phase gate up to
single-atom Rabi shifts. Furthermore, the fast-approach procedure is used to
design a path to significantly increase the fidelity of non-adiabatic transport
in a recent experiment. Also, the entanglement power of phase gates is
quantified.Comment: 7 pages, 4 figures. Phys. Rev. A (in press
Electron Magnetic Resonance: The Modified Bloch Equation
We find a modified Bloch equation for the electronic magnetic moment when the
magnetic moment explicitly contains a diamagnetic contribution (a magnetic
field induced magnetic moment arising from the electronic orbital angular
momentum) in addition to the intrinsic magnetic moment of the electron. The
modified Bloch is coupled to equations of motion for the position and momentum
operators. In the presence of static and time varying magnetic field
components, the magnetic moment oscillates out of phase with the magnetic field
and power is absorbed by virtue of the magnetic field induced magnetic moment,
even in the absence of coupling to the environment. We explicitly work out the
spectrum and absorption for the case of a state electron
Quantum Tunneling in the Wigner Representation
Time dependence for barrier penetration is considered in the phase space. An
asymptotic phase-space propagator for nonrelativistic scattering on a one -
dimensional barrier is constructed. The propagator has a form universal for
various initial state preparations and local potential barriers. It is
manifestly causal and includes time-lag effects and quantum spreading. Specific
features of quantum dynamics which disappear in the standard semi-classical
approximation are revealed. The propagator may be applied to calculation of the
final momentum and coordinate distributions, for particles transmitted through
or reflected from the potential barrier, as well as for elucidating the
tunneling time problem.Comment: 18 pages, LATEX, no figure
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Light-Fronts Approach to a Two-Center Time-Dependent Dirac Equation
Consider the relativistic scattering problem of an electron in the external field of two point-like charges (ions), moving on parallel, straight-line trajectories in opposite directions at speeds which approach the speed of light, and at an impact parameter 2b. An external-field approach to the influence of the ions on the electron is appropriate for peripheral impact parameters, heavy-ions, and high energies, where, to a very good approximation, the ions travel on parallel, straight-line trajectories, and ion recoil is negligible. We review here our recent work on this problem [1, 2, 3]. In section 2, following Ref. [2], we show that the two center time dependent Dirac equation for the electron reduces in the high energy limit to Eq. (26) with the interactions of Eq. (29). In section 3, following Ref. [1], we solve this equation off the light fronts i.e. for an electron that both initially and asymptotically is not co-moving with an ion. The main result of our work is the transition amplitude given by Eqs. (90) and (67). In section 4, we discuss the application of this solution to electromagnetic pair production in heavy ion collisions, which we have used, for example, in Ref. [3], to explain recent experimental results. We note that one should distinguish between electron-positron pairs produced so that they are co-moving with the ions and those that are not. The two cases differ experimentally. They also differ theoretically, because they are described by different asymptotic boundary conditions. We have solved the problem only for electron-positron pairs that are not co-moving with the ions. Our solution to the two center Dirac equation in the high energy limit was confirmed by different methods, including a Green function approach [4], and resummation of the perturbation series [5]. The application to pair production on the other hand, has raised some controversy, which is also discussed in section 4. Section 5 concludes