A CrC^{r} Closing Lemma for a Class of Symplectic Diffeomorphisms

We prove a $C^r$ closing lemma for a class of partially hyperbolic symplectic diffeomorphisms. We show that for a generic $C^r$ symplectic diffeomorphism, $r =1, 2, ...,$, with two dimensional center and close to a product map, the set of all periodic points is dense

Correcting symmetry imperfections in linear multipole traps

Multipole radio-frequency traps are central to collisional experiments in cryogenic environments. They also offer possibilities to generate new type of ion crystals topologies and in particular the potential to create infinite 1D/2D structures: ion rings and ion tubes. However, multipole traps have also been shown to be very sensitive to geometrical misalignment of the trap rods, leading to additional local trapping minima. The present work proposes a method to correct non-ideal potentials, by modifying the applied radio-frequency amplitudes for each trap rod. This approach is discussed for the octupole trap, leading to the restitution of the ideal Mexican-Hat-like pseudo-potential, expected in multipole traps. The goodness of the compensation method is quantified in terms of the choice of the diagnosis area, the residual trapping potential variations, the required adaptation of the applied radio-frequency voltage amplitudes, and the impact on the trapped ion structures. Experimental implementation for macroscopic multipole traps is also discussed, in order to propose a diagnostic method with respect to the resolution and stability of the trap drive. Using the proposed compensation technique, we discuss the feasibility of generating a homogeneous ion ring crystal, which is a measure of quality for the obtained potential well

Fast accumulation of ions in a dual trap

Transporting charged particles between different traps has become an important feature in high-precision spectroscopy experiments of different types. In many experiments in atomic and molecular physics, the optical probing of the ions is not carried out at the same location as the creation or state preparation. In our double linear radio-frequency trap, we have implemented a fast protocol allowing to shuttle large ion clouds very efficiently between traps, in times shorter than a millisecond. Moreover, our shuttling protocol is a one-way process, allowing to add ions to an existing cloud without loss of the already trapped sample. This feature makes accumulation possible, resulting in the creation of large ion clouds. Experimental results show, that ion clouds of large size are reached with laser-cooling, however, the described mechanism does not rely on any cooling process

Parallel ion strings in linear multipole traps

Additional radio-frequency (rf) potentials applied to linear multipole traps create extra field nodes in the radial plane which allow one to confine single ions, or strings of ions, in totally rf field-free regions. The number of nodes depends on the order of the applied multipole potentials and their relative distance can be easily tuned by the amplitude variation of the applied voltages. Simulations using molecular dynamics show that strings of ions can be laser cooled down to the Doppler limit in all directions of space. Once cooled, organized systems can be moved with very limited heating, even if the cooling process is turned off

Lorentz Beams

A new kind of tridimensional scalar optical beams is introduced. These beams are called Lorentz beams because the form of their transverse pattern in the source plane is the product of two independent Lorentz functions. Closed-form expression of free-space propagation under paraxial limit is derived and pseudo non-diffracting features pointed out. Moreover, as the slowly varying part of these fields fulfils the scalar paraxial wave equation, it follows that there exist also Lorentz-Gauss beams, i.e. beams obtained by multipying the original Lorentz beam to a Gaussian apodization function. Although the existence of Lorentz-Gauss beams can be shown by using two different and independent ways obtained recently from Kiselev [Opt. Spectr. 96, 4 (2004)] and Gutierrez-Vega et al. [JOSA A 22, 289-298, (2005)], here we have followed a third different approach, which makes use of Lie's group theory, and which possesses the merit to put into evidence the symmetries present in paraxial Optics.Comment: 11 pages, 1 figure, submitted to Journal of Optics

Structural Stability of Asymptotic Lines on Surfaces Immersed in R3

AbstractIn this paper are studied immersions of surfaces into to R3 whose nets of asymptotic lines are topologically undisturbed under small perturbations of the immersion. These immersions are called structurally asymptotic stable. Sufficient conditions to belong to this class are established here. These conditions focus on the stable patterns around parabolic points, parabolic separatrix connections, periodic asymptotic lines (including those that intercept the parabolic lines) as well the exclusion of recurrent asymptotic lines. The class of immersions that are structurally stable in this sense is open in the C5-topology

Bound state structure and electromagnetic form factor beyond the ladder approximation

We investigate the response of the bound state structure of a two-boson system, within a Yukawa model with a scalar boson exchange, to the inclusion of the cross-ladder contribution to the ladder kernel of the Bethe-Salpeter equation. The equation is solved by means of the Nakanishi integral representation and light-front projection. The valence light-front wave function and the elastic electromagnetic form factor beyond the impulse approximation, with the inclusion of the two-body current, generated by the cross-ladder kernel, are computed. The valence wave function and electromagnetic form factor, considering both ladder and ladder plus cross-ladder kernels, are studied in detail. Their asymptotic forms are found to be quite independent of the inclusion of the cross-ladder kernel, for a given binding energy. The asymptotic decrease of form factor agrees with the counting rules. This analysis can be generalized to fermionic systems, with a wide application in the study of the meson structure.Comment: 19 pages, 6 figures, submitted to Phys. Lett.