Subtractive renormalization of the NN interaction in chiral effective theory up to next-to-next-to-leading order: S waves

We extend our subtractive-renormalization method in order to evaluate the 1S0 and 3S1-3D1 NN scattering phase shifts up to next-to-next-to-leading order (NNLO) in chiral effective theory. We show that, if energy-dependent contact terms are employed in the NN potential, the 1S0 phase shift can be obtained by carrying out two subtractions on the Lippmann-Schwinger equation. These subtractions use knowledge of the the scattering length and the 1S0 phase shift at a specific energy to eliminate the low-energy constants in the contact interaction from the scattering equation. For the J=1 coupled channel, a similar renormalization can be achieved by three subtractions that employ knowledge of the 3S1 scattering length, the 3S1 phase shift at a specific energy and the 3S1-3D1 generalized scattering length. In both channels a similar method can be applied to a potential with momentum-dependent contact terms, except that in that case one of the subtractions must be replaced by a fit to one piece of experimental data. This method allows the use of arbitrarily high cutoffs in the Lippmann-Schwinger equation. We examine the NNLO S-wave phase shifts for cutoffs as large as 5 GeV and show that the presence of linear energy dependence in the NN potential creates spurious poles in the scattering amplitude. In consequence the results are in conflict with empirical data over appreciable portions of the considered cutoff range. We also identify problems with the use of cutoffs greater than 1 GeV when momentum-dependent contact interactions are employed. These problems are ameliorated, but not eliminated, by the use of spectral-function regularization for the two-pion exchange part of the NN potentialComment: 40 pages, 21 figure

Four-path interference and uncertainty principle in photodetachment microscopy

We study the quantal motion of electrons emitted by a pointlike monochromatic isotropic source into parallel uniform electric and magnetic fields. The two-path interference pattern in the emerging electron wave due to the electric force is modified by the magnetic lens effect which periodically focuses the beam into narrow filaments along the symmetry axis. There, four classical paths interfere. With increasing electron energy, the current distribution changes from a quantum regime governed by the uncertainty principle, to an intricate spatial pattern that yields to a semiclassical analysis.Comment: submitted to Europhysics Letter

Matter Wave Scattering and Guiding by Atomic Arrays

We investigate the possibility that linear arrays of atoms can guide matter waves, much as fiber optics guide light. We model the atomic line as a quasi-1D array of s wave point scatterers embedded in 2D. Our theoretical study reveals how matter wave guiding arises from the interplay of scattering phenomena with bands and conduction along the array. We discuss the conditions under which a straight or curved array of atoms can guide a beam focused at one end of the array.Comment: Submitted to Phys. Rev.

The Coulomb Interaction between Pion-Wavepackets: The piplus-piminus Puzzle

The time dependent Schr\"odinger equation for $\pi^+$--$\pi^-$ pairs, which are emitted from the interaction zone in relativistic nuclear collisions, is solved using wavepacket states. It is shown that the Coulomb enhancement in the momentum correlation function of such pairs is smaller than obtained in earlier calculations based on Coulomb distorted plane waves. These results suggest that the experimentally observed positive correlation signal cannot be caused by the Coulomb interaction between pions emitted from the interaction zone. But other processes which involve long-lived resonances and the related extended source dimensions could provide a possible explanation for the observed signal.Comment: 12 pages, LaTeX, 1 figur

Renormalization in Nonrelativistic Quantum Mechanics

The importance and usefulness of renormalization are emphasized in nonrelativistic quantum mechanics. The momentum space treatment of both two-body bound state and scattering problems involving some potentials singular at the origin exhibits ultraviolet divergence. The use of renormalization techniques in these problems leads to finite converged results for both the exact and perturbative solutions. The renormalization procedure is carried out for the quantum two-body problem in different partial waves for a minimal potential possessing only the threshold behavior and no form factors. The renormalized perturbative and exact solutions for this problem are found to be consistent with each other. The useful role of the renormalization group equations for this problem is also pointed out.Comment: 16 page

Electron Entanglement via a Quantum Dot

This Letter presents a method of electron entanglement generation. The system under consideration is a single-level quantum dot with one input and two output leads. The leads are arranged such that the dot is empty, single electron tunneling is suppressed by energy conservation, and two-electron virtual co-tunneling is allowed. This yields a pure, non-local spin-singlet state at the output leads. Coulomb interaction is the nonlinearity essential for entanglement generation, and, in its absence, the singlet state vanishes. This type of electron entanglement is a four-wave mixing process analogous to the photon entanglement generated by a Chi-3 parametric amplifier.Comment: 4 page

Path Integrals for Potential Scattering

Two path integral representations for the $T$-matrix in nonrelativistic potential scattering are derived and proved to produce the complete Born series when expanded to all orders. They are obtained with the help of "phantom" degrees of freedom which take away explicit phases that diverge for asymptotic times. In addition, energy conservation is enforced by imposing a Faddeev-Popov-like constraint in the velocity path integral. These expressions may be useful for attempts to evaluate the path integral in real time and for alternative multiple scattering expansions. Standard and novel eikonal-type high-energy approximations and systematic expansions immediately follow.Comment: 31 pages, 3 figures, Latex;v2: typo in eq. (4.6) corrected, references updated;v3: misprints corrected, small changes in text following referee comments and PR style conventions (except some idiosyncrasies), matches published version + typo correction in eq. (88

Quantum manipulation via atomic-scale magnetoelectric effects

Magnetoelectric effects at the atomic scale are demonstrated to afford unique functionality. This is shown explicitly for a quantum corral defined by a wall of magnetic atoms deposited on a metal surface where spin-orbit coupling is observable. We show these magnetoelectric effects allow one to control the properties of systems placed inside the corral as well as their electronic signatures; they provide alternative tools for probing electronic properties at the atomic scale

Detection and Cloaking of Molecular Objects in Coherent Nanostructures Using Inelastic Electron Tunneling Spectroscopy

We address quantum invisibility in the context of electronics in nanoscale quantum structures. We make use of the freedom of design that quantum corrals provide and show that quantum mechanical objects can be hidden inside the corral, with respect to inelastic electron scattering spectroscopy in combination with scanning tunneling microscopy, and we propose a design strategy. A simple illustration of the invisibility is given in terms of an elliptic quantum corral containing a molecule, with a local vibrational mode, at one of the foci. Our work has implications to quantum information technology and presents new tools for nonlocal quantum detection and distinguishing between different molecules.Comment: 5 pages, 4 figures, accepted in the Nano Letter