Pulsed Quantum Tunneling with Matter Waves

In this report we investigate the macroscopic quantum tunneling of a Bose condensate falling under gravity and scattering on a Gaussian barrier that could model a mirror of far-detuned sheet of light. We analyze the effect of the inter-atomic interaction and that of a transverse confining potential. We show that the quantum tunneling can be quasi-periodic and in this way one could generate coherent Bose condensed atomic pulses. In the second part of the report, we discuss an effective 1D time-dependent non-polynomial nonlinear Schrodinger equation (NPSE), which describes cigar-shaped condensates. NPSE is obtained from the 3D Gross-Pitaevskii equation by using a variational approach. We find that NPSE gives much more accurate results than all other effective 1D equations recently proposed.Comment: 9 pages, 5 figures, report for the X International Laser Physics Workshop, Seminar on Bose-Einstein Condensation of Trapped Atoms, Moscow, July 3-7, 200

Classical and Quantum Perturbation Theory for two Non--Resonant Oscillators with Quartic Interaction

We study the classical and quantum perturbation theory for two non--resonant oscillators coupled by a nonlinear quartic interaction. In particular we analyze the question of quantum corrections to the torus quantization of the classical perturbation theory (semiclassical mechanics). We obtain up to the second order of perturbation theory an explicit analytical formula for the quantum energy levels, which is the semiclassical one plus quantum corrections. We compare the "exact" quantum levels obtained numerically to the semiclassical levels studying also the effects of quantum corrections.Comment: 11 pages, Latex, no figures, to be published in Meccanic

Condensate fraction in metallic superconductors and ultracold atomic vapors

We investigate the condensate density and the condensate fraction of conduction electrons in weak-coupling superconductors by using the BCS theory and the concept of off-diagonal-long-range-order. We discuss the analytical formula of the zero-temperature condensate density of Cooper pairs as a function of Debye frequency and energy gap, and calculate the condensate fraction for some metals. We study the density of Cooper pairs also at finite temperature showing its connection with the gap order parameter and the effects of the electron-phonon coupling. Finally, we analyze similarities and differences between superconductors and ultracold Fermi atoms in the determination of their condensate density by using the BCS theory.Comment: 14 pages, 1 figure, 1 table, to be published in 'Fermions: Flavors, Properties, and Types' (Nova Science Publishers, New York)

Chaos Suppression in the SU(2) Yang--Mills--Higgs System

We study the classical chaos--order transition in the spatially homogenous SU(2) Yang--Mills--Higgs system by using a quantal analog of Chirikov's resonance overlap criterion. We obtain an analytical estimation of the range of parameters for which there is chaos suppression.Comment: LaTex, 10 pages, to be published in Phys. Rev.

3D BEC Bright Solitons under Transverse Confinement: Analytical Results with the Nonpolynomial Schrodinger Equation

The Bose-Einstein condensate (BEC) of a dilute gas of bosons is well described by the three-dimensional Gross-Pitaevskii equation (3D GPE), that is a nonlinear Schrodinger equation. By imposing a transverse confinement the BEC can travel only in the cylindrical axial direction. We show that in this case the BEC with attractive interaction admits a 3D bright soliton solution which generalizes the text-book one, that is valid in the one-dimensional limit (1D GPE). Contrary to the 1D case, the 3D bright soliton exists only below a critical number of Bosons that depends on the extent of confinement. Finally, we find that the 3D bright soliton collapses if its density excedes a critical value. Our results are obtained by using a nonpolynomial Schrodinger equation (NPSE), an effective one-dimensional equation derived from the 3D GPE.Comment: 4 pages, presented to the 5th International School/Conference 'Let's Face Chaos through Nonlinear Dynamics', Maribor, July 2002, to be published in Progress in Theoretical Physics Supplemen

Parametric Resonance Phenomena in Bose-Einstein Condensates: Breaking of Macroscopic Quantum Self-Trapping

We analyze the periodic tunneling of a Bose-Einstein condensate in a double-well potential which has an oscillating energy barrier. We show that the dynamics of the Bose condensate critically depends on the frequency $\omega$ of the oscillating energy barrier. In the regime of periodic macroscopic quantum tunneling (PMQT) with frequency $\omega_J$, the population imbalance of the condensate in the two wells can be enhanced under the condition of parametric resonance $\omega = 2 \omega_J$. Instead, in the regime of macroscopic quantum self-trapping (MQST), we find that MQST can be reduced or suppressed under the condition of parametric resonance between the frequency $\omega$ of the energy barrier and the frequency $\omega_{ST}$ of oscillation through the barrier of the very small fraction of particles which remain untrapped during MQST.Comment: 9 pages, 3 figures, prepared for the 'Laser Physics Workshop 2000', seminar on 'Bose-Einstein Condensation of Trapped Atoms', Bratislava, to be published in Laser Physic

Instabilities, Point Attractors and Limit Cycles in a Inflationary Universe

We study the stability of a scalar inflaton field and analyze its point attractors in the phase space. We show that the value of the inflaton field in the vacuum is a bifurcation parameter and prove the possible existence of a limit cycle by using analytical and numerical arguments.Comment: Latex, 11 pages, 3 figures (available upon request), to be published in Modern Physics Letters

Reply to a Comment on "the Role of Dimensionality in the Stability of a Confined Condensed Bose Gas"

As pointed out by the authors of the comment quant-ph/9712046, in our paper quant-ph/9712030 we studied in detail the metastability of a Bose-Einstein Condensate (BEC) confined in an harmonic trap with zero-range interaction. As well known, the BEC with attractive zero-range interaction is not stable but can be metastable. In our paper we analyzed the role of dimensionality for the metastability of the BEC with attractive and repulsive interaction.Comment: 4 pages, Latex, no figure

Enhancement of four reflection shifts by a three-layer surface plasmon resonance

We investigate the effect of a surface plasmon resonance on Goos-Hanchen and Imbert-Fedorov spatial and angular shifts in the reflection of a light beam by considering a three-layer system made of glass, gold and air. We calculate these spatial and angular shifts as a function of the incidence angle showing that they are strongly enhanced in correspondence of the resonant angle. In particular, we find giant spatial and angular Goos-Hanchen shits for the p-wave light close to the plasmon resonance. We also predict a similar, but less pronounced, resonant effect on spatial and angular Imbert-Fedorov shifts for both s-wave and p-wave light.Comment: 4 pages, 4 figures, accepted for publication in Phys. Rev.