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 $p$ 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

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