Collapse and Bose-Einstein condensation in a trapped Bose-gas with negative scattering length

We find that the key features of the evolution and collapse of a trapped Bose condensate with negative scattering length are predetermined by the particle flux from the above-condensate cloud to the condensate and by 3-body recombination of Bose-condensed atoms. The collapse, starting once the number of Bose-condensed atoms reaches the critical value, ceases and turns to expansion when the density of the collapsing cloud becomes so high that the recombination losses dominate over attractive interparticle interaction. As a result, we obtain a sequence of collapses, each of them followed by dynamic oscillations of the condensate. In every collapse the 3-body recombination burns only a part of the condensate, and the number of Bose-condensed atoms always remains finite. However, it can comparatively slowly decrease after the collapse, due to the transfer of the condensate particles to the above-condensate cloud in the course of damping of the condensate oscillations.Comment: 11 pages, 3 figure

Dynamics of dark solitons in elongated Bose-Einstein condensates

We find two types of moving dark soliton textures in elongated Bose-Einstein condensates: non-stationary kinks and proper dark solitons. The former have a curved notch region and rapidly decay by emitting phonons and/or proper dark solitons. The proper moving solitons are characterized by a flat notch region and we obtain the diagram of their dynamical stability. At finite temperatures the dynamically stable solitons decay due to the thermodynamic instability. We develop a theory of their dissipative dynamics and explain experimental data.Comment: ~ 5 pages, 1 figur

Solitons, solitonic vortices, and vortex rings in a confined Bose-Einstein condensate

Quasi-one-dimensional solitons that may occur in an elongated Bose-Einstein condensate become unstable at high particle density. We study two basic modes of instability and the corresponding bifurcations to genuinely three-dimensional solitary waves such as axisymmetric vortex rings and non-axisymmetric solitonic vortices. We calculate the profiles of the above structures and examine their dependence on the velocity of propagation along a cylindrical trap. At sufficiently high velocity, both the vortex ring and the solitonic vortex transform into an axisymmetric soliton. We also calculate the energy-momentum dispersions and show that a Lieb-type mode appears in the excitation spectrum for all particle densities.Comment: RevTeX 9 pages, 9 figure

Quantum fluctuations in coupled dark solitons in trapped Bose-Einstein condensates

We show that the quantum fluctuations associated with the Bogoliubov quasiparticle vacuum can be strongly concentrated inside dark solitons in a trapped Bose Einstein condensate. We identify a finite number of anomalous modes that are responsible for such quantum phenomena. The fluctuations in these anomalous modes correspond to the `zero-point' oscillations in coupled dark solitons.Comment: 4 pages, 3 figure

Lieb Mode in a Quasi One-Dimensional Bose-Einstein Condensate of Atoms

We calculate the dispersion relation associated with a solitary wave in a quasi-one-dimensional Bose-Einstein condensate of atoms confined in a harmonic, cylindrical trap in the limit of weak and strong interactions. In both cases, the dispersion relation is linear for long wavelength excitations and terminates at the point where the group velocity vanishes. We also calculate the dispersion relation of sound waves in both limits of weak and strong coupling.Comment: 4 pages, 2 ps figures, RevTe

The spectral properties of non-condensate particles in Bose-condensed atomic hydrogen

The strong spin-dipole relaxation, accompanying BEC in a gas of atomic hydrogen, determines the formation of a quasistationary state with a flux of particles in energy space to the condensate. This state is characterized by a significant enhancement of the low-energy distribution of non-condensate particles resulting in a growth of their spatial density in the trap. This growth leads to the anomalous reconstruction of the optical spectral properties of non-condensate particles.Comment: revised, 4 pages, RevTeX, 2 figure

Simulation of a stationary dark soliton in a trapped zero-temperature Bose-Einstein condensate

We discuss a computational mechanism for the generation of a stationary dark soliton, or black soliton, in a trapped Bose-Einstein condensate using the Gross-Pitaevskii (GP) equation for both attractive and repulsive interaction. It is demonstrated that the black soliton with a "notch" in the probability density with a zero at the minimum is a stationary eigenstate of the GP equation and can be efficiently generated numerically as a nonlinear continuation of the first vibrational excitation of the GP equation in both attractive and repulsive cases in one and three dimensions for pure harmonic as well as harmonic plus optical-lattice traps. We also demonstrate the stability of this scheme under different perturbing forces.Comment: 7 pages, 15 ps figures, Final version accepted in J Low Temp Phy