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

Three-body recombination of ultra-cold atoms to a weakly bound ss level

We discuss three-body recombination of ultra-cold atoms to a weakly bound $s$ level. In this case, characterized by large and positive scattering length $a$ for pair interaction, we find a repulsive effective potential for three-body collisions, which strongly reduces the recombination probability and makes simple Jastrow-like approaches absolutely inadequate. In the zero temperature limit we obtain a universal relation, independent of the detailed shape of the interaction potential, for the (event) rate constant of three-body recombination: $\alpha_{\rm rec}=3.9\hbar a^4/m$, where $m$ is the atom mass.Comment: 10 pages, 3 Postscript figure

Antiproton-Hydrogen annihilation at sub-kelvin temperatures

The main properties of the interaction of ultra low-energy antiprotons ($E\le10^{-6}$ a.u.) with atomic hydrogen are established. They include the elastic and inelastic cross sections and Protonium (Pn) formation spectrum. The inverse Auger process ($Pn+e \to H+\bar{p}$) is taken into account in the framework of an unitary coupled-channels model. The annihilation cross-section is found to be several times smaller than the predictions made by the black sphere absorption models. A family of $\bar{p}H$ nearthreshold metastable states is predicited. The dependence of Protonium formation probability on the position of such nearthreshold S-matrix singularities is analysed. An estimation for the $H\bar{H}$ annihilation cross section is obtained.Comment: latex.tar.gz file, 22 pages, 9 figure

Evolution and global collapse of trapped Bose condensates under variations of the scattering length

We develop the idea of selectively manipulating the condensate in a trapped Bose-condensed gas, without perturbing the thermal cloud. The idea is based on the possibility to modify the mean field interaction between atoms (scattering length) by nearly resonant incident light or by spatially uniform change of the trapping magnetic field. For the gas in the Thomas-Fermi regime we find analytical scaling solutions for the condensate wavefunction evolving under arbitrary variations of the scattering length $a$. The change of $a$ from positive to negative induces a global collapse of the condensate, and the final stages of the collapse will be governed by intrinsic decay processes.Comment: 4 pages, LaTeX, other comments are at http://WWW.amolf.nl/departments/quantumgassen/TITLE.HTM

On the stability of standing matter waves in a trap

We discuss excited Bose-condensed states and find the criterion of dynamical stability of a kink-wise state, i.e., a standing matter wave with one nodal plane perpendicular to the axis of a cylindrical trap. The dynamical stability requires a strong radial confinement corresponding to the radial frequency larger than the mean-field interparticle interaction. We address the question of thermodynamic instability related to the presence of excitations with negative energy.Comment: 4 pages, 3 figure

Bose-Einstein condensation in trapped dipolar gases

We discuss Bose-Einstein condensation in a trapped gas of bosonic particles interacting dominantly via dipole-dipole forces. We find that in this case the mean-field interparticle interaction and, hence, the stability diagram are governed by the trapping geometry. Possible physical realisations include ultracold heteronuclear molecules, or atoms with laser induced electric dipole moments.Comment: 4 pages, 4 figure

Influence of nearly resonant light on the scattering length in low-temperature atomic gases

We develop the idea of manipulating the scattering length $a$ in low-temperature atomic gases by using nearly resonant light. As found, if the incident light is close to resonance with one of the bound $p$ levels of electronically excited molecule, then virtual radiative transitions of a pair of interacting atoms to this level can significantly change the value and even reverse the sign of $a$. The decay of the gas due to photon recoil, resulting from the scattering of light by single atoms, and due to photoassociation can be minimized by selecting the frequency detuning and the Rabi frequency. Our calculations show the feasibility of optical manipulations of trapped Bose condensates through a light-induced change in the mean field interaction between atoms, which is illustrated for $^7$Li.Comment: 12 pages, 1 Postscript figur

Collapse dynamics of trapped Bose-Einstein condensates

We analyze the implosion and subsequent explosion of a trapped condensate after the scattering length is switched to a negative value. Our results compare very well qualitatively and fairly well quantitatively with the results of recent experiments at JILA.Comment: 4 pages, 3 figure

Superfluid pairing in a polarized dipolar Fermi gas

We calculate the critical temperature of a superfluid phase transition in a polarized Fermi gas of dipolar particles. In this case the order parameter is anisotropic and has a nontrivial energy dependence. Cooper pairs do not have a definite value of the angular momentum and are coherent superpositions of all odd angular momenta. Our results describe prospects for achieving the superfluid transition in single-component gases of fermionic polar molecules.Comment: 12 pages, 2 figure