Dynamic Critical Phenomena in Trapped Bose Gases

Nonlinear dynamics of a trapped Bose-Einstein condensate, subject to the action of a resonant external field, is studied. This field produces a spatio-temporal modulation of the trapping potential with the frequency close to the transition frequency between the ground state and a higher energy level. The evolution equations of fractional populations display a kind of critical phenomena at a critical line on the manifold of the system parameters. It is demonstrated that there exists a direct analogy between dynamical instability at this line and critical phenomena at a critical line of a related averaged system.Comment: Latex file, 7 pages, no figure

Coupling vortex dynamics with collective excitations in Bose-Einstein Condensates

Here we analyze the collective excitations as well as the expansion of a trapped Bose-Einstein condensate with a vortex line at its center. To this end, we propose a variational method where the variational parameters have to be carefully chosen in order to produce reliable results. Our variational calculations agree with numerical simulations of the Gross-Pitaevskii equation. The system considered here turns out to exhibit four collective modes of which only three can be observed at a time depending of the trap anisotropy. We also demonstrate that these collective modes can be excited using well established experimental methods such as modulation of the s-wave scattering length

Topological Coherent Modes in Trapped Bose Gas

The report reviews the problem of topological coherent modes, which are nonlinear collective states of Bose-condensed atoms. Such modes can be generated by means of alternating external fields, whose frequencies are in resonance with the transition frequencies between the related modes. The Bose gas with generated topological coherent modes is a collective nonlinear analog of a resonant atom. Such systems exhibit a variety of nontrivial effects, e.g.: interference fringes, interference current, mode locking, dynamic transitions, critical phenomena, chaotic motion, harmonic generation, parametric conversion, atomic squeezing, and entanglement production.Comment: 10 pages, Latex file; Plenary Talk, International Conference on Atomic Physics, Rio de Janeir