Trapped ions are considered one of the best candidates to perform quantum information processing. By interacting them with laser beams they are, somehow, easy to manipulate, which makes them an excellent choice for the production of nonclassical states of their vibrational motion, the reconstruction of quasiprobability distribution functions, the production of quantum gates, etc. However, most of these effects have been produced in the so-called low intensity regime, this is, when the Rabi frequency (laser intensity) is much smaller than the trap frequency. Because of the possibility to produce faster quantum gates in other regimes it is of importance to study this system in a more complete manner, which is the motivation for this contribution. We start by studying the way ions are trapped in Paul traps in and review the basic mechanisms of trapping. Then we show how the problem may be completely solved for trapping states; i.e., we find (exact) eigenstates of the full Hamiltonian. We show how in the low intensity regime Jaynes-Cummings and anti-Jaynes-Cummings interactions may be obtained, without using the rotating wave approximation and analyze the medium and high intensity regimes were dispersive Hamiltonians are produced. The traditional approach (low intensity regime) is also studied and used for the generation of non-classical states of the vibrational of the vibrational wavefunction. In particular, we show how to add and subtract vibrational quanta to an initial state, how to produce specific superpositions of number states and how to generate NOON states for the two-dimensional vibration of the ion. It is also shown how squeezing may be measured. The time dependent problem is studied by using Lewis-Ermakov methods, we give a solution to the problem when the time dependence of the trap is considered and also analyze an specific (artificial) time dependence that produces squeezing of the initial vibrational wave function. A way to mimic the ion-laser interaction via classical optics is also introduced.
Abstract:We present a classical analog of quantum optical deformed oscillators in arrays of waveguides. The normal modes of these onedimensional photonic crystals are given in terms of Jacobi polynomials. We show that it is possible to attack the problem via factorization by exploiting the corresponding quantum optical model. This allows us to provide an unbroken supersymmetric partner of the proposed Jacobi lattices. Thanks to the underlying SU(1, 1) group symmetry of the lattices, we present the analytic propagators and impulse functions for these one-dimensional photonic crystals.
Field enhancement and reflectivity of S-polarized Hermite-Gaussian beams from a rectangular groove ruled on a planar, perfectly conducting surface are analyzed by use of a modal theory. We show a novel effect in which S resonances are manifested by the appearance of sharp dips in the scattered intensity. We propose a relationship for the location of these minima in the scattered intensity with a precision better than 10 During the last few years in solid-state physics, great interest has grown regarding the relationship between Raman scattering and surface polaritons. ' By now, it is widely accepted that excitation of surface polaritons (which enhances the local-field intensity near the metal surface) is the main origin of surface-enhanced Raman scattering (SERS). This fact has motivated the study of the electric field near surface irregularities; a review isare not known to exist in nonmagnetic materials, it is interesting to investigate whether field enhancement is present with this polarization.Recently, in solid-state physics, infinitely conducting gratings have received attention because it was found theoretically that a silver grating gives practically the same results as for a perfectly conducting grating. 5 Wirgin and Maradudin treated an infinitely conducting lamellar grating, obtaining significant electric-field enhancements. However, they did not find any trace of S resonances in the far-field intensity, as occur with P-polarized radiation. This last negative result had already been presented by Andrewartha, Fox, and Wilson some years before.In this paper we present exact numerical calculations for the interaction of S-polarized beam waves of finite cross section with one groove ruled on a flat perfectly conducting screen. As incident beams of finite cross section we consider Hermite-Gaussian beams of arbitrary order, ' where the lowest order is an ordinary Gaussian beam. ' " As was pointed out by Marcuse, ' these beams are very important since laser modes have the shape of Hermite-Gaussian functions. To our knowledge, beams of finite cross section have not yet been considered in the study of the electric-field enhancement (S or P polarization). Our numerical experiments show that the proximity to 5-resonant wavelengths is indicated by dips in the reflected intensity, suggesting a simple and practical method for the 1ocation of these S resonances. It is important to remark that these observed minima in the far-field intensity are not related to any absorption of energy; in fact, a redistribution of energy takes place. We also propose a relationship for the location of these dips in the scattered intensity with a precision better than 10 The geometry of our system is shown in Fig. 1. We consider a rectangular groove ruled on a flat perfectly con-g+oo
We use the propagation of a conveniently shaped Gaussian beam in a GRIN media to mimic a quantum cavity filled with a Kerr medium. This is attained by introducing a second-order correction to the paraxial propagation of the beam. An additional result is that a Gaussian beam propagating in GRIN media may split into two Gaussian beams, corresponding to the generation of superposition of coherent states (Schrödinger cat states) in the cavity filled with the Kerr medium.
The short range revival of an arbitrary monochromatic optical field, which propagates in a quadratic GRIN rod, is a well-known effect that is established assuming the first-order approximation of the propagation operator. We discuss the revival and multiple splitting of an off-axis Gaussian beam propagating to relatively long distances in a quadratic GRIN medium. These effects are obtained assuming the second-order approximation of the propagation operator in this medium.
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