Exactly solvable one-qubit driving fields generated via non-linear equations

Using the Hubbard representation for $SU(2)$ we write the time-evolution operator of a two-level system in the disentangled form. This allows us to map the corresponding dynamical law into a set of non-linear coupled equations. In order to find exact solutions, we use an inverse approach and find families of time-dependent Hamiltonians whose off-diagonal elements are connected with the Ermakov equation. The physical meaning of the so-obtained Hamiltonians is discussed in the context of the nuclear magnetic resonance phenomeno

Leaky modes of waveguides as a classical optics analogy of quantum resonances

A classical optics waveguide structure is proposed to simulate resonances of short range one-dimensional potentials in quantum mechanics. The analogy is based on the well known resemblance between the guided and radiation modes of a waveguide with the bound and scattering states of a quantum well. As resonances are scattering states that spend some time in the zone of influence of the scatterer, we associate them with the leaky modes of a waveguide, the latter characterized by suffering attenuation in the direction of propagation but increasing exponentially in the transverse directions. The resemblance is complete since resonances (leaky modes) can be interpreted as bound states (guided modes) with definite lifetime (longitudinal shift). As an immediate application we calculate the leaky modes (resonances) associated with a dielectric homogeneous slab (square well potential) and show that these modes are attenuated as they propagate.Comment: The title has been modified to describe better the contents of the article. Some paragraphs have been added to clarify the result

Superpositions of bright and dark solitons supporting the creation of balanced gain and loss optical potentials

Bright and dark solitons of the cubic nonlinear Schrodinger equation are used to construct complex-valued potentials with all-real spectrum. The real part of these potentials is equal to the intensity of a bright soliton while their imaginary part is defined by the product of such soliton with its concomitant, a dark soliton. Considering light propagation in Kerr media, the real part of the potential refers to the self-focusing of the signal and the imaginary one provides the system with balanced gain-and-loss rates.Comment: 6 figures, 17 pages, LaTeX file. The manuscript has been re-organized (abstract, introduction and conclusions rewritten), and it now includes an appendix with detailed calculations of some relevant results reported in the paper. New references were adde

Dynamical Equations, Invariants and Spectrum Generating Algebras of Mechanical Systems with Position-Dependent Mass

We analyze the dynamical equations obeyed by a classical system with position-dependent mass. It is shown that there is a non-conservative force quadratic in the velocity associated to the variable mass. We construct the Lagrangian and the Hamiltonian for this system and find the modifications required in the Euler-Lagrange and Hamilton's equations to reproduce the appropriate Newton's dynamical law. Since the Hamiltonian is not time invariant, we get a constant of motion suited to write the dynamical equations in the form of the Hamilton's ones. The time-dependent first integrals of motion are then obtained from the factorization of such a constant. A canonical transformation is found to map the variable mass equations to those of a constant mass. As particular cases, we recover some recent results for which the dependence of the mass on the position was already unnoticed, and find new solvable potentials of the P\"oschl-Teller form which seem to be new. The latter are associated to either the su(1,1) or the su(2) Lie algebras depending on the sign of the Hamiltonian

Position dependent mass Scarf Hamiltonians generated via the Riccati equation

Producción CientíficaThe construction of position dependent mass Scarf Hamiltonians of the trigonometric as well as the hyperbolic types is addressed by means of the factorization method and the Riccati equation. These Hamiltonians are shown to be independent of the ordering parameter of the kinetic term. Additionally, new families of Hamiltonians with the Scarf spectrum are also determined by supersymmetry. Some examples for masses with and without singularities are considered to illustrate our results

Completeness and Nonclassicality of Coherent States for Generalized Oscillator Algebras

The purposes of this work are (1) to show that the appropriate generalizations of the oscillator algebra permit the construction of a wide set of nonlinear coherent states in unified form; and (2) to clarify the likely contradiction between the nonclassical properties of such nonlinear coherent states and the possibility of finding a classical analog for them since they are P-represented by a delta function. In (1) we prove that a class of nonlinear coherent states can be constructed to satisfy a closure relation that is expressed uniquely in terms of the Meijer G-function. This property automatically defines the delta distribution as the P-representation of such states. Then, in principle, there must be a classical analog for them. Among other examples, we construct a family of nonlinear coherent states for a representation of the su(1,1) Lie algebra that is realized as a deformation of the oscillator algebra. In (2), we use a beam splitter to show that the nonlinear coherent states exhibit properties like anti-bunching that prohibit a classical description for them. We also show that these states lack second order coherence. That is, although the P-representation of the nonlinear coherent states is a delta function, they are not full coherent. Therefore, the systems associated with the generalized oscillator algebras cannot be considered `classical' in the context of the quantum theory of optical coherence.Comment: 26 pages, 10 figures, minor changes, misprints correcte

Group approach to the paraxial propagation of Hermite–Gaussian modes in a parabolic medium

Física Teórica. Atómica y Óptic

Spherical harmonic expansions of the Earth's gravitational potential to degree 360 using 30' mean anomalies

Two potential coefficient fields that are complete to degree and order 360 have been computed. One field (OSU86E) excludes geophysically predicted anomalies while the other (OSU86F) includes such anomalies. These fields were computed using a set of 30' mean gravity anomalies derived from satellite altimetry in the ocean areas and from land measurements in North America, Europe, Australia, Japan and a few other areas. Where no 30' data existed, 1 deg x 1 deg mean anomaly estimates were used if available. No rigorous combination of satellite and terrestrial data was carried out. Instead advantage was taken of the adjusted anomalies and potential coefficients from a rigorous combination of the GEML2' potential coefficient set and 1 deg x 1 deg mean gravity anomalies. The two new fields were computed using a quadrature procedure with de-smoothing factors. The spectra of the new fields agree well with the spectra of the fields with 1 deg x 1 deg data out to degree 180. Above degree 180 the new fields have more power. The fields have been tested through comparison of Doppler station geoid undulations with undulations from various geopotential models. The agreement between the two types of undulations is approximately + or - 1.6 m. The use of a 360 field over a 180 field does not significantly improve the comparison. Instead it allows the comparison to be done at some stations where high frequency effects are important. In addition maps made in areas of high frequency information (such as trench areas) clearly reveal the signal in the new fields from degree 181 to 360