Two-mode effective interaction in a double-well condensate

We investigate the origin of a disagreement between the two-mode model and the exact Gross-Pitaevskii dynamics applied to double-well systems. In general this model, even in its improved version, predicts a faster dynamics and underestimates the critical population imbalance separating Josephson and self-trapping regimes. We show that the source of this mismatch in the dynamics lies in the value of the on-site interaction energy parameter. Using simplified Thomas-Fermi densities, we find that the on-site energy parameter exhibits a linear dependence on the population imbalance, which is also confirmed by Gross-Pitaevskii simulations. When introducing this dependence in the two-mode equations of motion, we obtain a reduced interaction energy parameter which depends on the dimensionality of the system. The use of this new parameter significantly heals the disagreement in the dynamics and also produces better estimates of the critical imbalance.Comment: 5 pages, 4 figures, accepted in PR

Dark soliton collisions in a toroidal Bose-Einstein condensate

We study the dynamics of two gray solitons in a Bose-Einstein condensate confined by a toroidal trap with a tight confinement in the radial direction. Gross-Pitaevskii simulations show that solitons can be long living objects passing through many collisional processes. We have observed quite different behaviors depending on the soliton velocity. Very slow solitons, obtained by perturbing the stationary solitonic profile, move with a constant angular velocity until they collide elastically and move in the opposite direction without showing any sign of lowering their energy. In this case the density notches are always well separated and the fronts are sharp and straight. Faster solitons present vortices around the notches, which play a central role during the collisions. We have found that in these processes the solitons lose energy, as the outgoing velocity turns out to be larger than the incoming one. To study the dynamics, we model the gray soliton state with a free parameter that is related to the soliton velocity. We further analyze the energy, soliton velocity and turning points in terms of such a free parameter, finding that the main features are in accordance with the infinite one-dimensional system.Comment: 15 pages, 11 figures. Accepted in PR

Benchmarking the Variational Reduced Density Matrix Theory in the Doubly Occupied Configuration Interaction Space with Integrable Pairing Models

The variational reduced density matrix theory has been recently applied with great success to models within the truncated doubly occupied configuration interaction space, which corresponds to the seniority zero subspace. Conservation of the seniority quantum number restricts the Hamiltonians to be based on the SU(2) algebra. Among them there is a whole family of exactly solvable Richardson-Gaudin pairing Hamiltonians. We benchmark the variational theory against two different exactly solvable models, the Richardson-Gaudin-Kitaev and the reduced BCS Hamiltonians. We obtain exact numerical results for the so-called PQGT N-representability conditions in both cases for systems that go from 10 to 100 particles. However, when random single-particle energies as appropriate for small superconducting grains are considered, the exactness is lost but still a high accuracy is obtained.Fil: Rubio García, A.. Instituto de Estructura de la Materia; España. Consejo Superior de Investigaciones Científicas; EspañaFil: Alcoba, Diego Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Capuzzi, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Dukelsky, J.. Consejo Superior de Investigaciones Científicas; España. Instituto de Estructura de la Materia; Españ

Pauli blocking and final-state interaction in electron-nucleus quasielastic scattering

The nucleon final-state interaction in inclusive electron-nucleus quasielastic scattering is studied. Based on the unitarity equation satisfied by the scattering-wave operators, a doorway model is developed to take into account the final-state interaction including the Pauli blocking of nucleon knockout. The model uses only experimental form factors as the input and can be readily applied to light- and medium-mass nuclei. Pauli blocking effects in these latter nuclei are illustrated with the case of the Coulomb interaction. Significant effects are noted for beam energies below ~ 350 MeV and for low momentum transfers.Comment: 16 pages, 6 figure

Structure of vortices in two-component Bose-Einstein condensates

We develop a three-dimensional analysis of the phase separation of two-species Bose-Einstein condensates in the presence of vorticity within the Thomas-Fermi approximation. We find different segregation features according to whether the more repulsive component is in a vortex or in a vortex-free state. An application of this study is aimed at describing systems formed by two almost immiscible species of rubidium-87 that are commonly used in Bose-Einstein condensation experiments. In particular, in this work we calculate the density profiles of condensates for the same conditions as the states prepared in the experiments performed at JILA [Matthews et al., Phys. Rev. Lett. 83, 2498 (1999)]Comment: 4 pages, 3 figure

Barrier effects on the collective excitations of split Bose-Einstein condensates

We investigate the collective excitations of a single-species Bose gas at T=0 in a harmonic trap where the confinement undergoes some splitting along one spatial direction. We mostly consider onedimensional potentials consisting of two harmonic wells separated a distance 2 z_0, since they essentially contain all the barrier effects that one may visualize in the 3D situation. We find, within a hydrodynamic approximation, that regardless the dimensionality of the system, pairs of levels in the excitation spectrum, corresponding to neighbouring even and odd excitations, merge together as one increases the barrier height up to the current value of the chemical potential. The excitation spectra computed in the hydrodynamical or Thomas-Fermi limit are compared with the results of exactly solving the time-dependent Gross-Pitaevskii equation. We analyze as well the characteristics of the spatial pattern of excitations of threedimensional boson systems according to the amount of splitting of the condensate.Comment: RevTeX, 12 pages, 13 ps figure

A hybrid configuration interaction treatment based on seniority number and excitation schemes

We present a configuration interaction method in which the Hamiltonian of an N-electron system is projected on Slater determinants selected according to the seniority-number criterion along with the traditional excitation-based procedure. This proposed method is especially useful to describe systems which exhibit dynamic (weak) correlation at determined geometric arrangements (where the excitation-based procedure is more suitable) but show static (strong) correlation at other arrangements (where the seniority-number technique is preferred). The hybrid method amends the shortcomings of both individual determinant selection procedures, yielding correct shapes of potential energy curves with results closer to those provided by the full configuration interaction method.Fil: Alcoba, Diego Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires; ArgentinaFil: Torre, Alicia. Universidad del Pais Vasco; EspañaFil: Lain, Luis. Universidad del Pais Vasco; EspañaFil: Oña, Ofelia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico La Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; ArgentinaFil: Capuzzi, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires; ArgentinaFil: Van Raemdonck, Mario. University of Ghent; BélgicaFil: Bultinck, Patrick. University of Ghent; BélgicaFil: Van Neck, Dimitri. University Of Ghent; Bélgic