31 research outputs found
Stationary solutions of the one-dimensional nonlinear Schroedinger equation: I. Case of repulsive nonlinearity
All stationary solutions to the one-dimensional nonlinear Schroedinger
equation under box and periodic boundary conditions are presented in analytic
form. We consider the case of repulsive nonlinearity; in a companion paper we
treat the attractive case. Our solutions take the form of stationary trains of
dark or grey density-notch solitons. Real stationary states are in one-to-one
correspondence with those of the linear Schr\"odinger equation. Complex
stationary states are uniquely nonlinear, nodeless, and symmetry-breaking. Our
solutions apply to many physical contexts, including the Bose-Einstein
condensate and optical pulses in fibers.Comment: 11 pages, 7 figures -- revised versio
Quantum carpet interferometry for trapped atomic Bose-Einstein condensates
We propose an ``interferometric'' scheme for Bose-Einstein condensates using
near-field diffraction. The scheme is based on the phenomenon of intermode
traces or quantum carpets; we show how it may be used in the detection of weak
forces.Comment: 4 figures. Submitted to Phys. Rev.
Simple method for excitation of a Bose-Einstein condensate
An appropriate, time-dependent modification of the trapping potential may be
sufficient to create effectively collective excitations in a cold atom
Bose-Einstein condensate. The proposed method is complementary to earlier
suggestions and should allow the creation of both dark solitons and vortices.Comment: 8 pages, 7 figures, version accepted for publication in Phys. Rev.
Observed photodetachment in parallel electric and magnetic fields
We investigate photodetachment from negative ions in a homogeneous 1.0-T
magnetic field and a parallel electric field of approximately 10 V/cm. A
theoretical model for detachment in combined fields is presented. Calculations
show that a field of 10 V/cm or more should considerably diminish the Landau
structure in the detachment cross section. The ions are produced and stored in
a Penning ion trap and illuminated by a single-mode dye laser. We present
preliminary results for detachment from S- showing qualitative agreement with
the model. Future directions of the work are also discussed.Comment: Nine pages, five figures, minor revisions showing final publicatio
Stability of dark solitons in a Bose-Einstein condensate trapped in an optical lattice
We investigate the stability of dark solitons (DSs) in an effectively
one-dimensional Bose-Einstein condensate in the presence of the magnetic
parabolic trap and an optical lattice (OL). The analysis is based on both the
full Gross-Pitaevskii equation and its tight-binding approximation counterpart
(discrete nonlinear Schr{\"o}dinger equation). We find that DSs are subject to
weak instabilities with an onset of instability mainly governed by the period
and amplitude of the OL. The instability, if present, sets in at large times
and it is characterized by quasi-periodic oscillations of the DS about the
minimum of the parabolic trap.Comment: Typo fixed in Eq. (1): cos^2 -> sin^
A realistic example of chaotic tunneling: The hydrogen atom in parallel static electric and magnetic fields
Statistics of tunneling rates in the presence of chaotic classical dynamics
is discussed on a realistic example: a hydrogen atom placed in parallel uniform
static electric and magnetic fields, where tunneling is followed by ionization
along the fields direction. Depending on the magnetic quantum number, one may
observe either a standard Porter-Thomas distribution of tunneling rates or, for
strong scarring by a periodic orbit parallel to the external fields, strong
deviations from it. For the latter case, a simple model based on random matrix
theory gives the correct distribution.Comment: Submitted to Phys. Rev.
Dark soliton states of Bose-Einstein condensates in anisotropic traps
Dark soliton states of Bose-Einstein condensates in harmonic traps are
studied both analytically and computationally by the direct solution of the
Gross-Pitaevskii equation in three dimensions. The ground and self-consistent
excited states are found numerically by relaxation in imaginary time. The
energy of a stationary soliton in a harmonic trap is shown to be independent of
density and geometry for large numbers of atoms. Large amplitude field
modulation at a frequency resonant with the energy of a dark soliton is found
to give rise to a state with multiple vortices. The Bogoliubov excitation
spectrum of the soliton state contains complex frequencies, which disappear for
sufficiently small numbers of atoms or large transverse confinement. The
relationship between these complex modes and the snake instability is
investigated numerically by propagation in real time.Comment: 11 pages, 8 embedded figures (two in color
Nonlinear atom optics and bright gap soliton generation in finite optical lattices
We theoretically investigate the transmission dynamics of coherent matter
wave pulses across finite optical lattices in both the linear and the nonlinear
regimes. The shape and the intensity of the transmitted pulse are found to
strongly depend on the parameters of the incident pulse, in particular its
velocity and density: a clear physical picture for the main features observed
in the numerical simulations is given in terms of the atomic band dispersion in
the periodic potential of the optical lattice. Signatures of nonlinear effects
due the atom-atom interaction are discussed in detail, such as atom optical
limiting and atom optical bistability. For positive scattering lengths, matter
waves propagating close to the top of the valence band are shown to be subject
to modulational instability. A new scheme for the experimental generation of
narrow bright gap solitons from a wide Bose-Einstein condensate is proposed:
the modulational instability is seeded in a controlled way starting from the
strongly modulated density profile of a standing matter wave and the solitonic
nature of the generated pulses is checked from their shape and their
collisional properties
Experimental investigation of rubidium atoms above the field-ionization limit using a time-resolved wave-packet approach
THE QUADRATIC ZEEMAN EFFECT IN HYDROGEN : AN EXAMPLE OF SEMI-CLASSICAL QUANTIZATION OF A STRONGLY NON-SEPARABLE BUT ALMOST INTEGRABLE SYSTEM
La quantification semi-classique de systèmes à plusieurs dimensions est discutée à l'aide de la méthode d'Einstein-Brillouin-Keller (EBK) sur les tores invariants de l'espace des phases, puis par la méthode des familles infinies de trajectoires périodiques. Les notions de séparabilité, de systèmes classiques intégrables et non-intégrables sont introduites. L'intégrabilité approchée existant dans le cas de l'effet Zeeman quadratique est utilisée pour la quantification de ce problème à l'aide de la forme normale de Birkhoff-Gustavson.Semi-classical quantization of multidimensional systems is discussed both in terms of the Einstein-Brillouin-Keller quantization on invariant tori, and in terms of infinite families of periodic orbits. The notions of separability, integrability, and non-integrability of classical systems are introduced. An approximate integrability is used to quantize the quadratic Zeeman problem, via analytic calculation of the Birkhoff-Gustavson normal form