Ehrenfest theorem, Galilean invariance and nonlinear Schr\"odinger equations

Galilean invariant Schr\"odinger equations possessing nonlinear terms coupling the amplitude and the phase of the wave function can violate the Ehrenfest theorem. An example of this kind is provided. The example leads to the proof of the theorem: A Galilean invariant Schr\"odinger equation derived from a lagrangian density obeys the Ehrenfest theorem. The theorem holds for any linear or nonlinear lagrangian.Comment: Latex format, no figures, submitted to journal of physics

Parametric excitation of a Bose-Einstein condensate in a 1D optical lattice

We study the response of a Bose-Einstein condensate to a periodic modulation of the depth of an optical lattice. Using Gross-Pitaevskii theory, we show that a modulation at frequency Omega drives the parametric excitation of Bogoliubov modes with frequency Omega/2. The ensuing nonlinear dynamics leads to a rapid broadening of the momentum distribution and a consequent large increase of the condensate size after free expansion. We show that this process does not require the presence of a large condensate depletion. Our results reproduce the main features of the spectrum measured in the superfluid phase by Stoeferle et al., Phys. Rev. Lett. 92, 130403 (2004).Comment: 4 pages, 4 figures, more results added, to appear in PRA Rapid Communication

Shape deformations and angular momentum transfer in trapped Bose-Einstein condensates

Angular momentum can be transferred to a trapped Bose-Einstein condensate by distorting its shape with an external rotating field, provided the rotational frequency is larger than a critical frequency fixed by the energy and angular momentum of the excited states of the system. By using the Gross-Pitaevskii equation and sum rules, we explore the dependence of such a critical frequency on the multipolarity of the excitations and the asymmetry of the confining potential. We also discuss its possible relevance for vortex nucleation in rotating traps.Comment: 4 pages revtex, 2 figures include

How to measure the Bogoliubov quasiparticle amplitudes in a trapped condensate

We propose an experiment, based on two consecutive Bragg pulses, to measure the momentum distribution of quasiparticle excitations in a trapped Bose gas at low temperature. With the first pulse one generates a bunch of excitations carrying momentum $q$, whose Doppler line is measured by the second pulse. We show that this experiment can provide direct access to the amplitudes $u_{q}$ and $v_{q}$ characterizing the Bogoliubov transformations from particles to quasiparticles. We simulate the behavior of the nonuniform gas by numerically solving the time dependent Gross-Pitaevskii equation.Comment: 12 pages, 4 figures include

Detecting phonons and persistent currents in toroidal Bose-Einstein condensates by means of pattern formation

We theoretically investigate the dynamic properties of a Bose-Einstein condensate in a toroidal trap. A periodic modulation of the transverse confinement is shown to produce a density pattern due to parametric amplification of phonon pairs. By imaging the density distribution after free expansion one obtains i) a precise determination of the Bogoliubov spectrum and ii) a sensitive detection of quantized circulation in the torus. The parametric amplification is also sensitive to thermal and quantum fluctuations.Comment: 4 pages, 4 figures; new figures, revised version to appear as a Rapid Communication in Physical Review

Dispersion of Ripplons in Superfluid 4he

A detailed study of the dispersion law of surface excitations in liquid \hef at zero temperature is presented, with special emphasis to the short wave length region. The hybridization mechanism between surface and bulk modes is discussed on a general basis, investigating the scattering of slow rotons from the surface. An accurate density functional, accounting for backflow effects, is then used to determine the dispersion of both bulk and surface excitations. The numerical results are close to the experimental data obtained on thick films and explicitly reveal the occurrence of important hybridization effects between ripplons and rotons.Comment: 23 pages, REVTEX 3.0, 11 figures upon request, UTF-326/9

On Bose-Einstein condensate inside moving exciton-phonon droplets

We explore a nonlinear field model to describe the interplay between the ability of excitons to be Bose condensed and their interaction with other modes of a crystal. We apply our consideration to the long-living paraexcitons in Cu2O. Taking into account the exciton-phonon interaction and introducing a coherent phonon part of the moving condensate, we solve quasi-stationary equations for the exciton-phonon condensate. These equations support localized solutions, and we discuss the conditions for the inhomogeneous condensate to appear in the crystal. Allowable values of the characteristic width of ballistic condensates are estimated. The stability conditions of the moving condensate are analyzed by use of Landau arguments, and Landau critical parameters appear in the theory. It follows that, under certain conditions, the condensate can move through the crystal as a stable droplet. To separate the coherent and non-coherent parts of the exciton-phonon packet, we suggest to turn off the phonon wind by the changes in design of the 3D crystal and boundary conditions for the moving droplet.Comment: 13 pages, LaTeX, three eps figures are incorporated by epsf. submitted to Phys. Letters

Static Response Function for Longitudinal and Transverse Excitations in Superfluid Helium

The sum rule formalism is used to evaluate rigorous bounds for the density and current static response functions in superfluid helium at zero temperature. Both lower and upper bounds are considered. The bounds are expressed in terms of ground state properties (density and current correlation funtions) and of the interatomic potential. The results for the density static response significantly improve the Feynman approximation and turn out to be close to the experimental (neutron scattering) data. A quantitative prediction for the transverse current response is given. The role of one-phonon and multi-particle excitations in the longitudinal and transverse channels is discussed. (Phys.Rev.B, in press)Comment: 19 pages (plain TeX) and 3 Figures (postscript), UTF-26

Vortex nucleation in rotating BEC: the role of the boundary condition for the order parameter

We study the process of vortex nucleation in rotating two-dimensional BEC confined in a harmonic trap. We show that, within the Gross-Pitaevskii theory with the boundary condition of vanishing of the order parameter at infinity, topological defects nucleation occurs via the creation of vortex-antivortex pairs far from the cloud center, where the modulus of the order parameter is small. Then, vortices move towards the center of the cloud and antivortices move in the opposite direction but never disappear. We also discuss the role of surface modes in this process.Comment: 6 pages, 2 figure

Vortex energy and vortex bending for a rotating Bose-Einstein condensate

For a Bose-Einstein condensate placed in a rotating trap, we give a simplified expression of the Gross-Pitaevskii energy in the Thomas Fermi regime, which only depends on the number and shape of the vortex lines. Then we check numerically that when there is one vortex line, our simplified expression leads to solutions with a bent vortex for a range of rotationnal velocities and trap parameters which are consistent with the experiments.Comment: 7 pages, 2 figures. submitte